{^-■r^'f 


FOREST  FINANCE 


Guide  to  Lectures 
Delivered  at  the  Biltmore  Forest  School 

By  C.  A.  SCHENCK,  Ph.  D. 

FORESTER  TO  THE  BILTMORE  ESTATE 


■^  ^ 
\^<^      ^5*. 


1909 


THE  INLAND  PRESS 
ASHEVILLE,  N.  C. 


c^ 


FOREST  FINANCE 


Guide  to  Lectures 
Delivered  at  the  Biltmore  Forest  School 

By  C.  A.  SCHENCK,  Ph.  D. 

FORESTER  TO  THE  BILTMORE  ESTATE 


1909 


THE  INLAND  PRESS 
ASHEVILLE,  5.  C. 


Digitized  by  the  Internet  Archive 

in  2009  with  funding  from 

NCSU  Libraries 


http://www.archive.org/details/forestfinanceguiOOsche 


Biltmore,  N.  C,  January  1,  1909. 


In  usum  Delphini: 

The  Biltmore  lectures  on  Forest  Finance  appear  in  print  since  it  is  nec- 
essary to  place  in  the  hands  of  the  Biltmore  students  some  basal  findings  con- 
cerning the  financial  side  of  forestry,  which  findings  it  is  not  easy  for  them 
to  obtain  elsewhere. 

In  America,  forest  finance  is  and  will  be  the  most  important  branch  of 
forestry;  the  very  difficulty  of  the  financial  problems  involved  in  American 
forestry  is  enticing;  and  I  am  interested,  personally,  more  deeply  in  the  scien- 
tific and  practical  development  of  forest  finance  than  in  that  of  any  other 
branch  of  American  forestry. 

Special  students  desirous  to  attend  the  Biltmore  lectures  on  forest  finance, 
and  otherwise  excluded  from  the  Biltmore  School,  will  be  welcomed  at  Bilt- 
more hereafter. 

This  arrangement  is  made  for  the  reason  that  the  lecturer  is  anxious  to 
study  forest  finance  through  and  with  the  students — the  regulars  as  well  as 
the  specials. 

Co-operation  between  teacher  and  pupil  is  essential  to  the  development 
of  American  forest  finance. 

The  interest  tables  attached  to  this  book  are  obtained,  by  extraction  and 
addition,  from  those  published  by  the  Mutual  Life  Insurance  Company  of 
New  York. 

C.  A.  SCEENCE. 


FOREST  FINANCE 


SYNOPSIS  OF  PARAGRAPHS 

Par.  I.  Introduction; 

Par.  II.  Mathematical  principles  of  finance; 

Par.  III.  Increasing  or  decreasing  prices; 

Par.  IV.  Receipts  and  expenses  in  forestry; 

Par.  V.  Taxes; 

Par.  VI.  Protective  expenses; 

Par.  VII.  Capital  and  money; 

Par.  VIII.  Interest; 

Par.  IX.  Expectation  values; 

Par.  X.  Sale  values; 

Par.  XI.  Gauging  the  merits  of  an  investment; 

Par.  XII.  Maturity  of  trees. 


FOREST  FINANCE 


PARAGRAPH  1.— INTRODUCTSON. 

I.  Definition. 

Forest  Finance  deals  with  forestry  as  an  investment. 

Treated  as  a  branch  of  science  in  European  literature,  it  consists  of  two 
parts: 

First  Part:  Forest  Valuation  which  ascertains  the  values  of  forest  in- 
vestments and  the  values  of  their  components. 

Second  Part:  Forest  Statics  which  compares  the  investments  with  the 
returns  obtained. 

Forestry,  from  the  standpoint  of  a  commonweal  (federation,  state,  county, 
town,  city)  deals,  to  a  large  extent,  in  abstract  or  ideal  values, — values  which 
are  not  expressible  easily  in  dollars  and  cents.  It  neglects,  usually,  financial 
considerations  entirely  or  partially. 

With  the  private  owner  of  forests,  the  financial  outcome  of  his  invest- 
ments is  the  first  and  last  consideration.  The  priva!e  owner  cannot  be  ex- 
pected to  supply  this  country  with  forest  products  u:iless  forestry  is  as  remun- 
erative an  investment  as  agriculture  is  found  to  be,  or  as  manufacture  is  sup- 
posed to  be, — industries  which  supply  this  country  v/ith  food  products  and 
with  manufactured  products. 

The  mathematical  principles  involved  in  Forest  Finance  arc  identical  with 
those  confronting  the  bankers,  the  insurance  companies, — in  fact,  corironting 
all  business  men  and  all  business  enterprises  that  lock  ahead  into  the  future. 

Forest  statistics,  deficient  unfortunately  in  the  United  Stares  (as  in  any 
ether  country  of  rapid  development),  are  important  as  a  basis  for  financial 
calculations. 

Forestal  forecasfs  in  the  countries  famous  for  conservative  forestry  are 
made  easily  and  with  a  high  degree  of  certainty. 

In  Canada,  in  Russia,  and  generally  in  the  United  States,  such  is  not 
the  case. 

II.  History. 

Forest  Finance  is  one  of  the  most  modern  branches  of  forestry.  Abroad, 
i\  was  unknown,  or  unheeded  by  the  practitioners,  previous  to  Max  Pressler 
(about  1860).  Pressler's  theories  were  developed  and  enlarged  upon  by  Gus- 
tav  Heyer. 

Dr.  Wm.  Schlich's,  and  Prof.  Charles  Vv^immenauer's  writings  are  entirely 
in  line  with  Heyer's  teachings. 

Financial  considerations  were  despised  generally  by  European  foresters 
until  recently.  The  government  cf  Saxony  was  first  to  adopt  financial  suc- 
cess as  the  goal  of  its  forest  policy. 


sf-^ 


^  FOREST  FINANCE.  -  ^.   — 

III.     Literafure. 

The  only  book  on  forest  finance  written  ki  English  is  SGiilich''s  Vof.  IIT, 

Part  II. 

The  interest  tables  of  the  various  insurance  companies  may  be  used  to 
solve  forestal  equations,  in  preference  to  tables  of  logarithms, 

PARAGRAFH  IL— MATHEMATICAL  PRINCIPLES 
OF  FINANCE. 

The  ratio  existing  between  principal  invested  (V)  and  atnount  obtained" 
(N),  or  the  ratio  between  "pre- value"  and  "aft-value"  of  an  investment  is 
expressed  by  the  following  equations  [in  which  (p)  represents  the  rate  of  in- 
terest and  (n)  the  number  of  years  covered  by  the  investments}: — 

N    =  VXL  Op°'  (A) 

N 

V   -  ^    =     y-^-  (B) 

1.  Op''     <^      ..  ^  ^  ^      "//  ' 

N  ^ 

I.  Op«   =  (C) 

V 
By  payments  (a)  regularly  occurring  at  given  intervals  of  time  a  "geom- 
etrical progression"  is  formed  after  the  pattern 
a  +  ar  +  ar^  +  ar'  +  ar*  +  ar(n  -  1) 
The  summary  of  this  geometrical  progression  is 
r"—  1 

a — (Dl 

r  —  1 
If  the  last  term  of  the  progression  is  expressed  as  "I"  (with  the  view  to 
the  elimination  of  "n"),  the  summary  is 
/    r  I  —  a 


4. 


r  —  1 

might  be  designated  as  "the  term  beyond  the  last",  or  as  the  terns 
"before  whicTi  the  progression  stops". 

Similarly,  the  sum  total  of  periodical  payments  (R)  due  at  intervals  of 
(m)  years,  for  the  first  time  due  after  (a)  yep.rs  and  altogether  (n)  times  is, 
considered  as  a  pre-value, 

1.  Op™°— 1        1.  Op"'a 

R  X (E) 

1.  0pm  —  1  1.  Opmn 

On  the  other  hand,  for  the  aft-value  of  such  periodical  payments  (R), 
the  sum  total  is 

1.  Op««  —  1 

R  XI.  Opni-a  (F) 

1.  Op°J  —  1 
In  the  case  of  an  annuity,  (m)  and  (a)  are  equal  to  1.     Consequently, 
the  summary  of  such  annuities  considered  as  a  pre-value  is 


FOREST  FINANCE  7 

1.  Op"  —  1 

R  (G) 

1.  Op°XO.  Op 

The  aft-value  of  such  annuities  is 

1.  Opn  —  1 


(H) 
0.  Op 

The  aft-value  of  sixigle  payments,  annuities  and  periodical  payments  at 
the  end  of  an  indefinite  period  is  itself  indefinite     (  C^  ). 

The  pre-value  of  a  single  payment  due  after  an  indefinite  period  of  years 
is  equal  to  zero. 

The  pre-value  (V)  of  annuities  or  periodical  payments  running  for  an 
indefinite  number  of  years  is,  however,  something  very  definite,  namely,  dis- 
counted backwards  to  the  present  day,  in  the  case  of  an  annuity: 
R 

V   =  (I) 

0.  Op 
or 
0  R 


100  V 

It  appears  at  a  glance  that  this  pre-value  (V)  derived  from  never-failing 
annuities — is  merely  the  capital  from  which  a  perpetual  revenue  of  p%  is 
expected.  Unknowingly,  the  investor  usually  figures  at  indefinitely  long  per- 
iods of  never  failing  returns  when  capitalizing  such  returns  at  a  given  rate 
of  interest.  It  is  only  too  well  known,  however,  that  all  investments,  except- 
ing pure  real  estate  investments,  have  a  merely  temporary  lease  of  life.  As 
an  illustration,  we  might  mind  the  fact,  that  the  majority  of  all  insurance 
policies  are  surrendered, — the  insured  being  unable  to  pay  his  dues  when  he 
meets  with  financial  reverses :  Business  investments,  in  the  majority  of  cases, 
seem  to  end  unluckily  for  the  investor. 

The  pre-value  (V)  of  periodical  payments  (R)  hereafter  due  at  the  end 
of  every  'mth"  year  until  infinity  is 
R 

V    =  .  (J) 

1.  Op™  —  1 

The  influence  on  present  values  exercised  by  payments  (receipts  or  ex- 
penses), expected  after  100  and  more  years,  is  very  small. 

For  the  financial  prospects  of  an  enterprise,  the  current  expenses  and 
receipts  of  the  first  (n)  years  are 

(1.  op°  —  1) 
times  as  influential  as  the  current  expenses  and  receipts  of  any  and  all  years 
following  after  the  nth  year. 

The  above  factor  of  influence,  viz.     (1.  op°  —  1),  equals  10  within 
50  years,  in  case  of  5%  investments ; 
63  years,  in  case  of  4%  investments; 
83  years,  in  case  of  3%  investments. 


8  FOREST  FINANCE 

"PROVIDED  THAT  THE  RATE  OF  INTEREST  IS  HIGH,  THE  HAP- 
PENINGS OF  A  MORE  DISTANT  FUTURE  ARE  IMMATERIAL  TO  THE 
INVESTOR." 

The  following  is  a  synopsis  of  the  preceding  formulae,  wherein: — 

p  equals  rate  of  interest. 

n        "     number  of  payments. 

m       "     duration  of  periodical  intervals  between  two  payments. 

a        "    years  after  which  a  periodical  rental  is  due  for  the  first  time. 

R        "    rentals  or  payment. 

V        "    pre-value. 

N        "    aft-value. 


i 

At  the  end  (aft-value) 

At  the  beginning  (pre-value) 

A  sum  of  money 
equals 

V  X  l.Opn 

N 
l.Op" 

[  Periodical 
Siunmary      |    Payments 

RCl.Op"'"— 1) 

1.0pm_l 

R(1.0pnm_i)l.0pm-a 
(l.Opni — Dl.Opnni 

Temporary   ) 
Rentals             Annual 

Payments 

RCl.Op"— 1) 
O.Op 

Rd.Opn— 1) 
O.Op  X  l.Opn 

(  Periodical 
Summary     \  Payments 
of            J 

OO 

R  X  l.Opm-a 
1.0pm— 1 

Rentals          /   Annudl 

V  payments 

OO 

R 
O.Op 

No  capitalist  and  no  forester  is  forced  to  adopt  a  financial  formula  or 
equation  when  determining  the  merits  of  an  investment.  THE  EQUATION 
MERELY  ILLUSTRATES  A  LOGICAL  MANNER  OF  FINANCIAL  THINK- 
ING, WHICH  IS  GENERALLY  ADOPTED  BY  THE  INSURANCE  COMPAN- 
IES, BANKERS,   AND  FAR-SIGHTED  BUSINESS  MEN. 

PARAGRAPH  III.— INCREASING  OR  DECREASING  PRICES. 

Stumpage  prices  are  rising  in  America, — possibly  at  the  rate  at  which 
the  population  increases,  possibly  faster, — promising  to  reach  the  present 
European  level  within  a  few  decades  of  years.  Consequently,  stumpage  now 
worth  "S"  dollars  per  thousand  feet  will  be  worth  at  "x%"  rise,  after  "n" 
years,  Sxl.  Ox^. 

The  present  value  of  such  stumpage,  to  be  harvested  after  "n"  years,  ia 
discounted  backwards  at  "y"  per  cent,  and  amounts  to 
SXl.  Ox° 


1.  Oyo 


FOREST  FINANCE 

In  place  of  this  terra,   it  is  permissible  to  write: 
S 


1.  0(y  —  x)° 
provided  that  "x"  and  "y"  do  not  exceed,  say,  8%  and  provided  that  the  per- 
iod of  calculation  does  not  exceed  100  years. 

Mathematically,    the    substitution    is    incorrect;    for   practical    purposes, 
however,  it  is  permissible  within  certain  limits. 

If     X  equals  4.7% 

and  y       "      3% 

and  n       "       100  years, 
the  mistake  made  by  the  "short  cut"  equals  5.2%. 
The  mistake  increases: 

(1)  With  the  increase  of  the  price  percentage  (x)  and  discount  per- 
centage (y). 

(2)  With  increasing  discrepancy  between  price  percentage  (x)  and  dis- 
count percentage  (y) ; 

(3)  With  the  increasing  number  of  years  (n). 

Generally,  the  mistake  does  not  exceed  5%.     An  advantage  of  the  "short 
cut"  is  the  larger  scope  it  offers  to  financial  imagination  or  to  differences  of 
opinion  relative  to  the  rise  of  stumpage  prices  or  relative  to  the  proper  rate 
S  SXl.  OS-^ 

of  discount.     Thus,  might  be  interpreted  as     or  as 

1.  03°  1.  08° 

SXl.  04°  SXl.  03° 


or  as 


1.  07°  1.  06° 

"THE  BASAL  RATE  OF  INTEREST  IN  AN  EQUATION  MAY  NOT  REP- 
RESENT THE  DIVIDEND  WHICH  THE  OWNER  EXPECTS  TO  DERIVE 
FROM  HIS  INVESTMENTS." 

In  the  cases  just  given,  the  investor  will  realize  8%  if  stumpage  prices 
rise  at  5% ;  7%,  if  they  rise  at  4% ;  6%,  if  they  rise  at  3% ;  or  only  3%,  if  the 
stumpage  prices  do  not  rise  at  all. 

If  the  prices  are  increasing  at  the  SAME  rate  at  which  the  values  are 
discounted  backward,  the  summary  of  the  pre-values  is  (for  annuities  as  well 
as  for  intermittent  rentals),  nXR. 

l.op°» 
mth  year: 


l.op^ 


2mth  year:     R 


Summary    =  nXR. 

Obviously,  the  summary  of  prevalues,  in  this  case,  is  C30  for  indefinite 
rentals.  It  is  unreasonable  to  suppose,  that  prices  will  ALWAYS  rise  and 
continue  to  rise. 


10  FOREST  FINANCE 

The  growth  of  trees  expressed  in  dollars  and  cents  is  composed  of  the 
following  factors: 

A. — Increase  of  volume,  due  to  the  annual  formation  of  a  new  ring  or, 
better,  of  a  new  coat  all  over  the  old  body. 

B. — Increase  of  value,  the  larger  diameter  fetching  a  higher  price  per 
thousand  feet  board  measure  than  the  smaller  diameter  (difference 
in  value  of  different  sized  logs  at  the  same  time). 

C. — Increase  of  price  (difference  in  price  of  the  same  sized  logs  at  dif- 
ferent times),  due  to  an  increase  of  population,  to  increased  logging 
facilities  and  to  waning  supplies. 

The  forester  speaks  of  the  volume  increment,  the  value  increment  and 
the  price  increment  of  a  tree;  and  of  the  volume  increment  percentage  "a.%", 
the  value  increment  percentage  "b%",  and  the  price  increment  percentage 
"c%"  of  a  tree  or  of  a  forest. 

Thus,  a  tree  now  worth  "S"  dollars  is  worth  after  "n"  years  SXl.Oa° 
Xl.Ob'iXl.Oc^;  which  term  is  almost  equal  to  SXl.O  (a+b+c)^ 

In  the  case  of  young  and  sound  timber  all  percentages  can  be  assumed 
to  range  between  1%  and  4%. 

In  the  case  of  primeval  timber  of  large  diameter,  volume  and  value  in- 
crement is  insignificantly  small.  On  the  other  hand,  primeval  timber  is  getting 
scarce  so  rapidly  (walnut,  cherry,  white  pine,  yellow  poplar,  white  oak)  that 
a  large  price  increment  percentage  can  be  depended  upon. 

Learn  to  differentiate  between  the  merits  of  investments  in  first  growth 
and  of  investments  in  second  growth!! 

An  interesting  case  of  a  declining  VALUE  increment  may  be  found  in 
hickory  poles  at  a  time  at  which  they  begin  to  form  heartwood;  or  in  poplar 
poles  at  a  similar  time,  when  they  begin  to  be  less  fit  for  match  stock  or  for  fibre. 

An  interesting  case  of  declining  PRICE  increment  (aside  of  panics,  aban- 
doned use  of  given  woods,  replacement  of  one  species  by  another,  change  of 
tariff,  export  prohibition,  Panama  canal)  may  be  found  in  small  trees  left  by 
conservative  lumbering.  These  trees  had  a  better  value  BEFORE  than  AFTER 
the  breaking  up  of  the  means  of  transportation. 

PARAGRAPH  IV.— RECEIPTS  AND  EXPENSES 
IN  FORESTRY. 

I. — The  revenue  in  forestry  may  consist  of: — 

A. — Yields  derived  from  sale  or  lease  of  forest  pasture;  from  hunting 

privileges;  from  water  privileges  (power  or  reservoir);  from  mines, 

quarries,  peat  bogs,  etc.;  from  turpentine  and  maple  sugar  orchards; 

from  tan  bark,  cork,  mosses,  grasses,  pharmaceutical  herbs,  litter, 

nuts,  seeds  and  so  on. 
B. — Increasing  volume  of  growing  stock;   increasing  value  of  growing 

stock  and  of  soil  without  any  lumbering  (so-called  latent  yields). 
C. — Usually,  during  and  after  the  installation  period,  yields  obtained  from 

sale  of  wood  products,  notably, 


FOREST  FINANCE  11 

(a)  Stumpage  (French  system) ; 

(b)  Log  yards  (German  system) ; 

(c)  Manufactured  products  like  lumber,  staves,  shingles,  telephone 
posts,  ties,  blocks  for  carriages,  pulp  wood,  tannin,  fence  posts, 
etc.  (American  system). 

II. — Timber  yields  are  ascertained  by : — 

A. — Cruising  or  valuation  surveys. 

B. — Yield  tables  (applicable  only  to  even  aged  and  pure  forests,  fairly 
well  stocked). 

C. — Volume  tables  (applicable  only  to  sound  trees). 

D. — The  increment  percentage. 

In  the  United  States,  reliable  statistics  relative  to  the  growth  of  the  forests 
— especially  of  second  growth — and  of  the  trees  are  badly  lacking. 

ni. — Present  timber  values. 

The  present  values  of  timber  (stumpage  values)  depend,  for  a  given  species, 
on  the  expense  now  required  for  its  utilization, — notably  on  the  charges  for 
transportation  which  are  governed  by: 

A. — Distance  from  the  market. 

B. — Availability  of  water,  ice,  snow,  railroads  and  public  roads  as  means 
of  transportation. 

C. — Volume  of  stumpage  per  acre  and  volume  on  the  entire  tract. 

D. — Quality  of  the  logs  (percentage  of  firsts  and  seconds,  common,  cull, 
mill  cull,  etc.). 

£. — Climatic  conditions  (malarial  climates,  long  and  cold  winters,  short 
logging  seasons). 

F. — Specific  gravity  of  timber. 

In  the  far  backwoods,  stumpage  even   of  the  best  trees  frequently  has  a 
negative  value.     Near  the  market,  even  utterly  poor  trees  assume  a  positive 
value. 
IV.— Future  Timber  Values. 

The  study  of  future  timber  values  is  of  paramount  importance  with  the 
forestal  investor.  Similarly  *^he  capitalist  is  interested  in  the  advancing  value 
of  real  estate,  the  coming  J  .idends  of  railroad  stock,  etc. 

He  must  consider 

A. — For  a  country :  The  probability  of  a  general  change  of  timber  prices 
due  to: 

a.  Competition  of  metals  and  stone  (building  stone). 

b.  Waning  virgin  supplies. 

c.  Importations  from  Canada,  the  tropics  and  Europe. 

d.  Increasing  population. 

e.  Coming  prosperity  or  coming  depression  of  all  industries. 

f.  New  uses  of  timber,  especially  in  the  spinning  and  weaving  in- 
dustries, in  the  food  industries,  in  the  production  of  alcohol. 

g.  Wages  rising  or  dropping. 
h.     Gold  standard. 

i.      Automobile  traction. 


12  FOREST  FINANCE 

B. — For  a  species:     The  possibility  of  price  alterations  in  favor  of  or  to 
the  detriment  of  a  species  locally  prevailing  (chestnut  in  Pisgah  For- 
est; spruce  in  the  Adirondacks;  cottonwood  in  Arkansas;  remember 
laws  causing    the    price   of    wood-alcohol  to  drop  from  67c  to  39c 
per  gallon  in  1907.) 
C. — For  a  locality :     The  chances  for  improved  access  to  a  special  market 
by  improved  railroads,   improved  navigation   (Panama  canal),  and 
improved  public  roads;  the  chances  for  the  opening  of  new  local 
markets,  or  for  enlarged  foreign  markets. 
Opinions  relative  to  future  developments  necessarily  differ  in  forestry 
as  well  as  in  agriculture,  railroading  and  industrial  establishments.     On  ex- 
change, such  fluctuations  and  such  diversity  of  opinion  are  particularly  pro- 
nounced. 

V. — The  expenses  in  forestry  are : 

A. — Ordinary  or  running  expenses,  viz., 

1.  Outlay  for  logging  and  milling; 

2.  Administrative  expenses; 

3.  Taxes; 

4.  Protective  expenses; 

5.  Maintenance  of  boundaries  and  land  marks; 

6.  Natural  or  artificial  reforestation  (this  expense  equals,  in  Ger- 
many, from  10% — 20%  of  the  net  stumpage  values  annually 
disposed  of); 

7.  Forest  pedagogy; 

8.  Up-keep  of  investments,  notably  of  the  means  of  transportation 

(this  expense  equals,  in  Germany,  from  5%  to  15%  of  the  net 
stumpage  values  annually  disposed  of). 
Many  of  these  ordinary  running  expenses  must  be  considered,  during  the 
installation  period,  as  extraordinary  investments. 
B. — Extraordinary  Investments. 

1.  Soil  and,  usually,  trees. 

2.  Permanent  means  of  transportation. 

3.  Wood  working  establishments. 

4.  Buildings,  farms,  pastures,  ochards. 

5.  Surveys  and  working  plans. 

6.  Fire  lanes. 

7.  Fences  for  pastures,  game,  etc. 

8.  Afforestation. 

Al!  over  the  world,  but  especially  so  in  the  United  States,  the  capital  now 
invested  in  a  forest  is  not  that  which  promises  to  yield  the  highest  rate  of  int- 
erest for  the  next  period  of  years.  The  principal  investment  requires  addi- 
tions here  and  reductions  there.  The  time  at  which  alterations  should  be 
made  depends  upon  local  factors  as  well  as  upon  personal  opinion. 

The  components  of  the  final  investment  in  conservative  forestry  are  those 
enumerated  under  B.— Naturally,  there  is  no  need  for  all  of  them  to  be  at 
hand  in  every  case.     The  share  which  each  component  takes  or  should  take 


FOREST  FINANCE  13 

in  ths  aggregate  investment,  again  depends  upon  local  conditions  and  upon 
personal  opinions. 

Forest  investments,  in  this  connection,  do  not  play  any  exceptional  part. 
In  agriculture,  e.  g.,  the  final  investments  are  composed  of  soil,  improvements, 
roads,  clearings,  live  stock,  machinery,  buildings,  etc.  Likewise,  mining  in- 
vestments do  not  consist  of  mineral  soil  merely;  but,  in  addition  to  soil,  of 
machinery,  buildings,  railroads,  shafts,  etc. 

A  forest  must  be  considered  "normal"  when  the  investment  which  it  rep- 
resents has  reached,  for  the  time  being,  in  the  owner's  opinion,  the  highest 
stage  of  relative  remunerativeness,  with  all  of  its  (the  investment's), 
components  balancing  in  proper  equilibrium.  Naturally,  the  owner  alone 
can  decide  whether  this  stage  is  act'ially  reached  or  not. 

PARAGRAPH  V.— TAXES. 

In  America  taxes  usually  depend  upon  the  market  value  of  a  taxable 
object  and  amount,  in  the  wooded  states,  to  about  19c  ad  valorem  of  the  same. 
If  the  market  value  '"V"  of  a  given  forest  grows  at  the  annual  rate  of  "x%" 
during  'n''  years,  the  taxes  (theoretically  at  least)  increase  likewise  at  the 
rate  of  ''x%'\  They  accumulate  at  the  rate  of  "p%"  in  such  a  manner  as 
to  amount,  at  the  year  "n",  to  the  sum  total 

V  1.0x°  —  1.0p« 

X Xl.Ox  (M) 

100         l.Ox  —  l.Op 

Case  I:  x     equals     p 

Then  the  aft-value  of  every  single  tax  payment  equals, 

V 

(1.0x1) 

100 

The  summary  of  the  aft-values  equals 

n   \ [l.Ox° 

/lOO    \ 

or  n%  of  the  forest  aft-value  (which  is  VXl.Ox°). 
Thus,  if  "n"  equals  25,  the  taxes  consume  }i  of  the  aft-value;  if  "n" 
equals  100,  the  taxes  consume  the  entire  aft-value. 
Case  II:  x  is  smaller  than  p 

Then  1.0x°  is  much  smaller  than  1.0p° ;  the  summary  is  much  larger  than 

V 

(1.0x°)  or  much  larger  than 

100 

n 

the  part  of  the  forest  aft-value. 

100 

Thus,  if  "n"  equals  25,  the  taxes  consume  more  than  }:{  of  the  aft-value; 
and  if  '"n"  equals  100,  the  taxes  consume  more  than  the  entire  aft- 
value. 


14  FOREST  FINANCE 

Case  III :  x    is  larger  than    p 

n 

Here  the  taxes  consume  less  than  the  part  of  the  aft-value,  e.  g., 

100  '       ^' 

if  "n"  equals  25,  the  taxes  consume  less  than  3^  of  the  aft-value; 
and  if  "n"  equals  100,  the  taxes  consume  less  than  the  entire  aft-value. 
Deductions  from  the  above: — 

RULE  I. 

Destructive  forestry  is  indicated  where  a  long  number  of  years  is  expected 
to  elapse  before  a  second  cut  can  be  obtained;  where  taxation  ad  valorem  is 
high;  where  the  value  of  the  forest  grows  slowly  (x  being  smaller  than  p). 

RULE  n. 

The  forester,  bent  on  forest  conservation,  must  endeavor  to  shorten  the 
period  of  waiting  between  cuts  by  leaving  sufficient  stumpage  and  sufficient 
means  of  transportation  to  allow  of  frequent  cuttings  within  the  same  forest. 

RULE  m. 

The  damaging  effect  of  taxation  depends  pre-eminently  on  the  period  of 
waiting;  the  rate  of  interest  being  more  irrelevant,  "x"  being  usually  equal 
to  or  close  to  "p".  After  the  wholesale  removal  of  the  primeval  forest,  the 
period  of  waiting  is  excessively  long.  The  forester's  activity  should  be  called 
upon  before  and  not  after  the  first  inroads  of  the  axe  into  the  primeval  woods. 

PARAGRAPH  VI.— PROTECTIVE  EXPENSES. 

The  influence  exercised  on  the  prospects  of  conservative  lumbering  by 
expenses  for  forest  protection  is  analogous  to  the  influence  of  taxes.  The 
decision  whether  and  what  protection  should  be  given  to  a  forest,  solely  rests 
with  the  owner. 

The  following  may  illustrate  the  influence  of  the  protective  expenses  on 
a  forest  conservatively  managed: 
FIRST.     An  unprotected  forest,  "V",  may  yield  an  annual  net  surplus  revenue 

"R"  as  long  as  it  escapes  fires  and  theft. 

R  y 

equals  or     lOOR  equals  yV 

V  100 

SECOND.  Sacrificing  annually  "D"  dollars  for  protection,  the  owner  retains 
a  revenue,  "R  —  D",  and  the  interest  percentage  "y"  is  reduced  to  "z" 
per  cent.,  whilst  "V"  remains  much  unchanged  as  long  as  no  fire  happens 
to  occur. 


100 


FOREST  FINANCE 


16 


THIRD. 


Hence 


and 

D           y  -z 

R           y 

If 

D     eqtials  8%  of  R 
Rs    equals     lOOD 
s        y  —  z 

then 
and 

100 


(N) 


(O) 


FIFTH. 

For  "y"  ranging  from  2%  to  8%  and  for  "s"  ranging  from  5%  to  30%, 
the  percentage  of  net  revenue  "z"  is  reduced  as  appears  in  the  table  following:— 


s  equals 

5% 

lO^c     I      16% 

..-, 

25% 

30% 

y  equals       2                                         |     19             1.8     j     1.7       |     1.6 

1.5       1       14 

y        -           3                                        1     2  85     1     2  7          2  55     |     2  4 

2  25     i       2  1 

y        "           4                                        1     38       !     3  6     1     3  4       i     3  2 

3.0              2  8 

y        •'           6                                        1     4.76     1     4.6     !     4.25     j     4.0 

3  75     1       3  6 

y        "           6                                         1     5.7       1     8.4     1     5.1       1     4.8 

4.6       1       4.2 

y        ••           7                                         1     6.66     1     63     j     5  95     |     5  6 

5.26     1       4.9 

y        ••           8                                         j     7.6       j     7.2     i     6.8       j     6.4 

6  0       1       6  6 

In  the  case  of  a  forest  which  does  not  yield  an  annual  surplus  revenue, 
the  influence  of  the  protective  expenses  is  somewhat  different  from  the  above, 
as  is  illustrated  by  the  following  considerations: — 
FIRST.     Such  aforest  "V"  grows  in  'n"  years  at  ■'x%"  to  a  value  of  VCl.Ox") 

wherein  "V"  equals  the  sale  value. 
SECOND.     The  same  forest  "V"  protected  at  an  annual  expense  of  "w"% 
shows  a  net  aft-value,  omitting  the  influence  of  taxes,  etc. 
w         (  1.0p°  —  1  ) 

V(1.0x°)  —  V  I ]■  (P) 

100       (      O.Op         ) 
where  "p"  equals  the  per  cent,  of  capitalization  selected  by  the  owner. 

THIRD.     The  sacrifice  brought  by  the  owner  for  protection's  sake  is: 


(1.0p°  —  1) 


(Q) 


16 


FOURTH.     If  the  ratio 


equals     (l-Op" 

4 


FOREST  FINANCE 
equals  3^,  then  the  sacrifice 


If  the  ratio     equals  1/10,  then  the  sacrifice  equals 

P 
V 

(1.0p°  -  1) 

10 

Absolutely  taken,  the  sacrifice  greatly  increases  with  the  length  of  the 
period  of  waiting.     Relatively  considered,  the  sacrifice  does  not  increase  nec- 
essarily. 
p    equals    4%  x    equals     5% 


n 

1.04"-1 

Sacrifice 
w      1 

P  ~4 

Sacrifice 
w       1 

p      10 

1.05" 

to  fl 

w        1 

nd  z 

w       1 
p  ~10 

l.Ozn 

l.Ozn 

z 

10  yr. 

.48 

.12V 

.05V 

1  63 

1.51 

1.58 

4.76 

•  20" 

1  19 

.30V 

.12V 

2  65 

2  35 

2  S3 

4.76 

f  SO" 

2.24 

.86V 

.22  V 

4.32 

3.72 

4  10 

4.8 

[40" 

3.80 
6.11 

.95V 

.3SV 

7.04 

6  09 

6  66 

4.8 

60" 

1.63V 

.61V 

11  47 

994 

10  86 

4.86 

The 
produced 
value, 
y  equals 


figures  in  the  last  and  third  last  columns  give  the  rate  of  interest 
in  a  forest  protected  at  an  annual  expenditure  of  w%  of  its  original 

the  rate  of  interest  produced  in  the  unprotected  forest  as  long  as 

all  goes  well. 
per  cent,  of  revenue  sacrificed  for  protection, 
the  original  sale  of  the  forest. 

number  of  years  that  elapse  before  the  forest  is  cut. 
rate  at  which  the  forest  grows  in  value,  if  fires  are  barred, 
rate  of  interest  expected  by  the  owner. 
per  cent,  of  the  original  value  spent  annually  for  protection, 
rate  of  interest  produced  in  the  protected  forest. 

PARAGRAPH  VII.— CAPITAL  AND  MONEY. 


A. 


Any  object  or  thing  having  earning  power  is  a  capital.     By  "earning 

power"  is  understood  the  power  to  furnish  commodities  coveted  by  man. 

B. — "Money"  is  not  "capital";  it  is  merely  the  "legalized  measure  of  values", 

and  hence  frequently  the  measure  of  "capital".     Different  countries  legal- 


FOREST  FINANCE  17 

ize  or  use  different  units  of  measure,  and  within  the  same  country,  time 

causes  the  unit  to  vary  (cattle  in  the  United  States;  platinum  in  Russia; 

silver  in  some  of  the  Latin  countries;  glass  pearls  with  the  Indians;  courie 

shells  with  the  Siamese). 

Money,  in  other  words,  is  nothing  but  a  unit  of  measuring,  having  func- 
tions like  those  of  the  yard,  the  bushel,  the  pound  (all  being  subject  to  fluc- 
tuations) to  wit,  the  functions  of  measuring. 
C— All  production  originates  with  nature,  and  all  capital  consists,  in  part,  of 

natural  creations  or  natural  objects,  namely: 

1.  Natural  gifts  (soil  and  soil  products) ; 

2.  Natural  forces  (wind,  water,  fire,  gravity,  electricity,  heat,  rainfall). 
D.— Accumulated  human  labor  forms,  usually,  a  part  of  a  capital  actuaUy 

producing  (field,  wind  mills  or  water  mills). 
E.— Merely  natural  capitals  to  which  no  human  labor  (accumulated)  is  at- 
tached, are  usually  unproductive;  although  their  earning  power  might  be 
at  hand  (most  of  our  waterfalls;  the  prairies  a  century  ago). 
Mines  and  fields,  without  the  addition  of  accumulated  labor,  cannot  prove 
their  earning  power.     The  forest  and  the  pasture— under  certain  conditions 
at  least  and  for  limited  periods— may  create  new  commodities  without  requir- 
ing labor  to  be  previously  performed.  <  .     ,, 
F  —As  long  as  the  population  increases,  the  individual's  share  in  the  "gifts 
and  in  the  "forces"  of  nature— especially  in  the  gifts— DECREASES  and 
the  units  of  such  gifts  and  forces  increase  in  value. 
On  the  other  hand,  capital  consisting  largely  of  accumulated  human  labor 
depreciates  under  the  same  circumstances. 

The  more  a  capital  consists  of- {^^^^::^ade}-'=°"'P°'''"*''    ^^'   ^'"" 
are  its  chances  to  gradually-  |">®jj  }  —in  (exchange)  value. 
Rule  a.      As  long  as  capital,  labor,  population  and  money  in  circulation  re- 
main the  same,  values  remain  the  same. 
Rule  b.      If  capital  alone  decreases  (population,  labor  and  money  stagnating) 
less  products  are  available  and  $1.00  can  buy  less  products  or  less 
capital  than  heretofore.     (This  rule  holds  good,  especiaUy,  in  the 
case  of  the  necessities  of  life.) 
Rule  c.      If  population  alone  grows  (capital  and  money  stagnating),  $1.00 
can  buy  less  natural  products  or  capital  than  heretofore  and  can 
buy  more  man-made  capital  or  products  than  heretofore  (since 
labor  is  cheapened). 
Rule  d.      If  money  alone  increases  (population  and  capital  stagnating),  $1.00 
can  buy  less  products,  labor  or  capital  than  heretofore. 
As  a  matter  of  fact,  population  and  circulating  money  are  on  the  increase 
in  the  United  States,  whilst    capital  consisting  of  natural  gifts  is  decreasing 
and  whilst  capital  consisting  of  natural  forces  remains  the  same. 
H.— All  economic  factors  combine  as  a  consequence  to  continuously  lessen 
the  purchasing  power  of  the  dollar  in  the  United  States.     The  legalized 


18  FOREST  FINANCE 

measure  of  value  getting  shorter  in  its  effect,  the  number  of  units  of  value 

(or  dollars)  equalling  a  capital  or  a  product  increase  necessarily. 
I.— Gold. 

The  world's  production  of  gold  (the  money  of  the  leading  nations)  has 
increased  and  continues  to  increase  at  an  alarming  rate.  This  increase  has 
had  the  tendency,  unavoidably,  of  cheapening  gold,  or  of  reducing  its  power 
to  purchase  other  goods. 

If  man  were  actually  to  realize  the  enormous  increase  of  the  production 
of  gold,  the  decline  of  its  purchasing  power  would  be  more  patent — it  would 
become  acute. 

A  commodity  (gold  is  a  commodity  like  silver  or  iron  or  wheat,  after  all) 
drops  in  value  at  a  time  when  it  is  known  (or  supposed)  to  be  produced  in  excess 
of  the  demand; — not  at  a  time  when  it  actually  happens  to  be  excessively 
produced. 

In  the  case  of  gold,  in  the  author's  opinion,  mankind  has  not  begun  to 
realize  the  enormous  increase  of  the  supply;  and  it  is  far  from  anticipating  a 
still  more  gigantic  increase  of  the  supply  in  the  near  future  at  a  time  when 
new  technical  and  chemical  methods  of  "gold  making"  come  into  play. 

A  demoralizing  "slump"  in  our  entire  monetary  system  is  unavoidable  as 
soon  as  gold  can  be  produced  at  a  greatly  reduced  expense  of  labor.  The 
knowledge  of  a  slight  over-production  causes  the  price  of  cereals  and  cotton 
and  lumber  to  decline  perceptibly;  similarly,  the  knowledge  of  a  slight  excess 
production  of  gold  must  cause  its  depreciation. 

In  the  past  decades,  this  depreciation  has  been  prevented  by  a  number  of 
countries  rapidly  adopting  the  gold  standard  and  accumulating  gold  in  their 
treasuries. 

In  the  future,  this  depreciation  must  be  marked.  If  the  purchasing  power 
of  gold  decreases  at  the  rate  of  2%  per  annum  (and  the  author  anticipates  a 
more  rapid  decline),  the  consequences  will  be: 

a.  for  the  possessor  of  bonds,  mortgages,  life  insurance  policies,  etc., 

a  heavy  loss  of  capital  as  well  as  of  interests. 

b.  for  a    "country  of  bondholders",   and  therefore  pre-emmently  for 

European  countries,  heavy  losses; 

c.  for  "countries  of  stockholders",  and  countries  rich  in  pastures  and 

forests  and  farms,  a  decided  superiority  over  others  not  so  blessed. 

A  man  owning  4%  bonds  rated  at  par  will  do  well — if  he  desires  to  remain 
equally  wealthy — to  consume  not  over  3-^  of  the  interests  obtained  and  to  re- 
invest the  other  3^2  with  a  view  to  counterbalancing  the  tendency  of  gold  to 
depreciate. 

Conclusions. 

A  man  owning  $100,000  cash  in  1908  is  less  wealthy  than  the  man 
owning  the  same  amount  in  1898. 

A  man  who  has  let  out,  in  1898,  $100,000  and  who  has  consumed  in  the 
meantime  all  interest  derived  therefrom,  is  getting  less  wealthy.  He  should 
have  saved  a  portion  of  the  interest  actually  obtained  adding  it  to  the  original 
$100,000. 


FOREST  FINANCE  IS 

On  the  other  hand,  a  man  letting  out,  in  1898,  10,000  acres  of  land  and 
retaining  them  in  1908  in  equal  productiveness,  is  absolutely  as  wealthy  now 
as  before;  relatively  wealthier  than  before,  although  he  was  allowed  to  con- 
sume all  interest  or  revenue  obtained  from  the  lease. 

PARAGRAPH  VIII.— INTEREST. 

I. — Definitions. 

A. — Interest  (gross)  is  the  price  paid  for  the  use  of  capital. 

B. — As  freight  is  the  price  of  "site-difference",  so  is  interest  the  price 

of  "time-difference". 
C. — Net  interest  is  the  difference  of  a  capital's  "earning  power"  at  the 
beginning  and  at  the  end  of  a  season  plus  the  value  of  the  product 
in  the  meantime  produced  by  capital  and  not  by  labor. 
D. — Interest  may  mean  either  the  net  or  the  gross  product  of  capital, 

i.  e.,  of  any  object  having  earning  power. 
E. — The  price  of  the  use    of   labor    equals  the  value  (of   product,  or  of 
capital)  which  the  employer  hopes  to  create  thereby. 

The   price   of  the  use  of   capital   equals   the  value  (of  product, 
or  of  new  capital)  which  the  employer  hopes  to  create  thereby. 
F. — Interest  is  the  product  of  capital;  its  price  is  the  price  of  the  product  I 
In  loans  of  capital,  it  is  usual  to  loan  the  "measure  of  capital"  (gold) 
and  to  turn  over  to  the  owner  thereof  the  "measure  of  the  product" 
(gold.) 
The  borrower  may  use  a  loan  to  pay  WAGES  and  in  that  case  he  ACT- 
UALLY borrows  LABOR,  reconvertmg  "ACCUMULATED"  labor  into  "RUN- 
NING" labor. 
n. — Gross  Interest  on  Money  Loans. 

This  is  the  product  of  capital  employed  in  another  man's  production. 
It  consists  of  the  following  parts: — 

a.  The  true,  net,  actual,  clear  yield  of  capital  "{%&)". 

b.  "Risk  quota",  or  remuneration  for  risk  taken,  or  capital  secretly 

repaid,  or  capital  apt  to  be  consumed  in  the  course  of  the  pro- 
duction. This  quota  is  meant  to  rebuild  that  much  of  the  origina 
capital  as  is  iiable  to  incidental  destruction  "(^b)". 

c.  Remuneration  for  labor,  financial  sagacity  and  discomforts  requiredl 
from  the  owner  in  harvesting  the  yield  of  capital  "(^c)". 

d.  Quota  which  must  be  saved  and  added  to  the  original  in  order  to 

allow  the  owner  to  remain  equally  wealthy  whilst  the  purchasing 
power  of  money  declines  "(td)". 
The  investing  capitalist  invariably  over-estimates  the  true  or  net  yields 
of  his  investment  ("^a)  and  proceeds  to  consume  Cb)  and  (*!d). 

Few  families  remain  equally  "wealthy"  in  the  long  run  excepting  those 
owning  entailed  real  estate. 

in. — Interest  on  merely  natural  investments  (farms)  consists  of  "(fa)"  and 
of  "(lie)".  The  risk  "(^b)"  is  little  since  the  soil,  at  least,  is  safe. 
There  is  no  "iW"- 


20  FOREST  FINANCE 

IV. — Interest  on  capital  consisting  of  accumulated  labor  has  a  very  large 
"(^b)".       This  is  proven  by  the  following: — 

1.  It  can  be  outranked  and  reduced  in  value  by  other  and  better  labor- 
accumulations  (e.  g.,  sulphite  fiber  process  superseding  soda  fiber 
process;  Southern  cotton  factories  outranking  Northern  cotton  fac- 
tories; steamships  superseding  sailing  craft). 

2.  The  real  necessities  of  life  are  more  a  soil  product  than  a  labor  pro- 
duct. In  the  case  of  unnecessary  articles,  fashions  and  inventions 
cause  continuous  fluctuations  of  the  remunerativeness  of  the  in- 
vestments producing  such  unnecessary  articles. 

3.  If  a  production,  basing  largely  on  accumulated  labor,  is  found  to  be 
remunerative,  it  is  at  once  overdone;  and  competition  kills  the  yields 
(e.  g.,  bicycle  manufacturing). 

4.  Labor-made  capital  (machinery)  is  usually  consumed  in  the  course 
of  the  production. 

V. — It  may  be  said  that  no  man  who  wishes  to  be  on  the  safe  side,  on  an  aver- 
age, should  annually  consume  over  2%  on  his  investment;  or  that  no  man 
should  rate  the  true  earning  power  of  his  investment  at  a  figure  exceed- 
ing 2%. 

The  financial  genius,  of  course,  can  do  better  and  can  credit  himself  with 
a  large  "(lie)";  he  foresees  the  development  of  the  future  correctly;  at  an 
outlay  of  $1,000,  for  instance,  he  creates  or  acquires  a  capital  producing 
$100  of  true  net  "{%&)",  which  is  worth  $5,000.  Thus,  he  owns  five  times 
as  much  as  before  at  the  end  of  the  production.  * 

Theoretically,  the  genius  obtains  wealth  by  buying  productive  capital 
actually  under-rated  by  the  majority  of  the  owners,  and  by  selling  productive 
capital  actually  over-rated  by  others.  The  blunderers  foresee  the  coming 
events  wrongly;  they  sell  on  a  rising  market,  and  they  buy  on  a  falling  market. 
During  the  year,  the  investors  change  their  opinion  frequently,  relative 
to  the  outlook  of  the  future;  hence  continuous  fluctuations  on  exchange.  The 
ratings  placed  by  two  men  on  the  same  investment  coincide  in  rare  cases  only; 
hence  few  transactions  on  exchange,  a  trade  being  made  only  when  two  men 
happen  to  agree. 

VI. — Additional  factors  influencing  the  rate  of  interest: — 

1.  Unhandy  credit  systems; 

2.  Partial  or  slow  courts; 

3.  Danger  of  foolish  legislation; 

4.  Amount  of  indestructible  assets. 

The  factors  1,  2  and  3  increase,  and  the  factor  4  decreases  the  rate  of 
interest. 

The  rate  of  interest  charged  for  loans  and  bonds  increases  whenever  the 
industries  prosper.  The  available  money  is  then  withdrawn  from  loans  and 
put  into  industrial  engagements. 

VII. — Limits  of  Interest. 

1.  The  lowest  limit  is  the  figure  at  which  the  owner  prefers  to  hide  or 
consume  his  belongings. 


FOREST  FINANCE  21 

2.  The  upper  limit  is  the  actual  effect  of  the  investment  for  which  means 
and  bounds  do  not  exist.  If  the  investment  cannot  be  duplicated 
(Standard  Oil),  the  rate  of  interest  becomes  a  personal  matter  being 
governed  by  the  capitalization  which  the  owners  choose  to  adopt. 

Vin. — The  net  or  true  interest 

1.  has  the  tendency  of  equalization 

A.  in  loans,  because  interest  is  merely  the  price  of  such  loans  re- 
sembling the  price  of  any  other  commodity; 

B.  in  investments,  because  universally  remunerative  investments 
are  soon  over-crowded  by  competition  where  duplication  is  pos- 
sible. Where  this  is  not  possible,  there  abnormal  revenue  is  at 
once  capitalized,  the  new  capital  value  being  added  to  the  ori- 
ginal ("watered  investments"); 

2.  has  the  tendency  of  sinking  because  the  wealth  of  the  nations  is 

rising  at  a  faster  rate  than  the  chances  at  remunerative  employment 
of  wealth. 

IX. — Justification  of  Interest. 

1.  The  Church,  since  325  A.  D.,  has  condemned  interest  after  Luke 

VI :  35.     In  the  early  Christian  era,  loans  for  consumption  only  were 
known,  not  loans  for  production. 

2.  After  Adam  Smith,  the  capitalist  would  not  care  to  take  any  risk, 
temporarily  parting  with  the  full  control  of  his  property,  if  he  did 
not  see  any  inducements. 

3.  After  Senior,  interests  are  payments  due  to  the  owner  for  abstaining 
from  the  immediate  consumption  of  his  property. 

4.  After  Marx  and  La  Salle,  interest  is  cut-off  from  the  wages  properly 
belonging  to  the  wage  earner. 

5.  Merely  natural  capitals  (deer,  buffalo,  trees,  grass  lands)  produce 
annually.  Thus,  interest  on  capital  is  natural, — is  part  of  the  econ- 
omy of  nature. 

X. — Rate  of  Interest  in  Forestry. 
1.     Conservative  Forestry. 

a.  There   is  no  "(Hb)"    or  "(Hd)"   to    be  deducted  from  the  gross 

rate  of  interest,  since  there  is  no  risk  and  no  influence  on  the 
investment  due  to  the  declining  purchasing  power  of  money. 

b.  The  rate  of  interest  compares  favorably  with  agricultural  interest 

because  the  products  of  the  forest  can  be  stored  free  of  cost, 
and  are  exposed  but  little  to  drought,  inundation,  boll  weevil, 
etc.     If  the  products  are  killed  by  storm,   fire  and  insects, 
forestry  can  bring  them  to  the  market,  usually,  at  a  scarcely 
reduced  price  (see  American  Lumberman,  September  19,  1908). 
The  rate  of  true  interest  in  conservative  forestry  is  about  23.^%  (in  Sax- 
ony, on  an  average  for  the  year  1905,  2  Vlo% ;    see  Thar.  Forst  Jahrbuch, 
1907,  1st  issue.)  and  compares  very  favorably  with  4%  on  bonds  and  6%  on 
industrial  investments. 


22  FOREST  FINANCE 

2.     Destructive  Forestry. 

The  net  revenue  cannot  be  separated  easily  from  the  capital  gradually 
withdrawn  from  the  forest.  If  only  soil  (S)  remains  after  complete  exhaus- 
tion, within  (n)  years,  of  a  forest  of  the  original  value  (Q)  whilst  surplus  re- 
ceipts, Ri,  R2,  R3,  etc.,  are  obtained  during  the  (n)  years  of  destructive  lum- 
bering, then  the  rate  of  interest,  (x),  is  illustrated  by  the  following  equation : — 
QXl.Ox>i=Rl  (1.0x°-l)+R2   (1.0x'i-2)+R3   (1.0x'>-3)+      .     .     .     Rn    +   S. 

XI. — Saxon  Statistics  show: — 

1.        That  the  State  forests  have  paid,  since  1816,  2%  net  on  the  annual 
average. 
2.    That  the  money  value  of  the  forest,  since  1816,  has  risen  by  3%  on 
the  annual  average,  a  rise  largely  due  to  the  declining  purchasing 
power  of  gold  and  partly  due  to  improvements  and  additional  in- 
vestments. 
Xn. — The  decision  in  the  problem  confronting  the  owner:     "Shall  I  practice 
conservative  forestry  or  destructive  forestry?"  must  be  based  on  the  true 
rate  of  net  interest  obtainable  from  the  one  and  from  the  other.     It  re- 
mains for  the  forester  to  demonstrate  the  difference  between  net  interest 
and  gross  interest. 

The  chances  for  conservatism  in  forestry  to  be  superior  to  radicalism 
are,  on  the  whole,  extremely  good  and  especially  so  in  the  United  States,  since 

1.  The  American  lumber  market  is  almost  continuously  overstocked 

beyond  its  digestive  capacity.  The  virgin  supplies  are  being  ex- 
hausted, and  are  apt  to  be  entirely  exhausted  by  1950.  In  the  mean- 
time the  stumpage  prices  of  all  good  timber  must  increase  steadily. 

2.  It  must  be  remembered  that  the  now  wealthy  lumbermen  have  made 
their  wealth  by  buying  stumpage  when  and  where  it  was  under- 
valued and  by  holding  it  for  a  number  of  years.  Fortunes  have 
never  been  made  by  any  particular  skill  in  lumbering,  milling  or 
sale  of  lumber. 

Strange  as  it  may  sound:     Inactivity  has  paid  better  in  the  case  of  in- 
vestments in  American  forestry  than  hard  work  spent  in  lumbering  and  milling. 
There  is  no  reason  to  anticipate  that  the  future  will  materially  differ 
from  the  past. 

XIII. — Interpretation  of  the  rate  of  interest  on  which  a  calculation  is  based: 
X 

1)        The  sum  may  mean 

l.op° 

a)  that  the  calculator  expects  with  a  faith  in  his  forecasts  expressed 
by  p%  receipts  or  expenses  (X)  to  occur  (n)  years  from  date 
of  calculation,  or 

b)  that  the  calculator  expects,  with  a  faith  in  his  forecasts  approx- 
imated by  (p+y),  receipts  or  expenses 

X 

or        XXl.oyo 

l.oy° 
to  occur  n  years  from  date  of  calculation. 


FOREST  FINANCE  28 

This  possibility  of  interpretation  allows  of  the  expression  of  widely  dif- 
ferent forecasts  by  a  mere  change  of  the  rate  of  interest  underlyiag  the  cal- 
culation. The  basal  rate  underlying  an  equation  does  not  or  need  not  design- 
ate the  actual  dividend  expected  by  the  calculator.  It  is  the  mathematical 
outcome  of  his  fears  and  his  hopes,  of  gloomy  and  of  rosy  anticipations. 

PARAGRAPH  IX.— EXPECTATION  VALUE. 

The  actual  value  of  any  object  to  its  owner,  or  to  anybody  else  (cow, 
house,  railroad  bonds,  mining  stock)  equals  the  pre-value  of  the  expected  ser- 
vices or  yields,  duninished  by  the  pre-value  of  the  expected  expense  required 
to  obtain  such  services  or  yields.  Obviously,  the  rate  of  discount  is  of  para- 
moimt  importance  relative  to  the  result  of  the  calculation.  'Individual  opin- 
ion" governs  the  rate  of  discount  as  well  as  the  anticipations^of  future  events. 

Values  rise  with  the  expectation  of  rising  yields,  of  sinkmg  expenses  and 
or  reduced  rates  of  interest,  and  vice  versa.  Obviously,  the  selection  of  the 
rate  of  interest,  and  the  forecasts  of  future  yields  and  expenses,  depend,  above 
all,  on  personal  opinions  which  may  be  pessimistic  or  optimistic,  bearish  or 
bullish. 

Applied  to  forestry,  we  find  the  following  expectation  values: 

1.  Value  of  a  regular  second  growth  forest  (m)  years  old: 

thna         thnb         thuc  f.c.  i-s.v. +V 

+ + + V 

1.0p«-™    l.Opb-m      l.Op'^-™  l.Op'^-™ 

wherein  thna,  thnb,  thnc  stands  for  thinnings  in  the  year  a,  b,  and 
c  of  the  forest;  f.c,  for  value  of  final  cut;  s.v.,  for  soil  value  after 
final  cut,  and  V  for  a  perpetual  rental  defraying  taxes  and  admini- 
strative expenses  reduced  by  annual  receipts  for  leases,  etc. 

2.  The  value  of  bare,  absolute  forest  soil,  planted  up  at  an  expense  of 

"pig"  and  weeded  at  an  expense  of  "weed"  equals 

thna  X  LOp*"-*  +  thnb  X  l.Op'^b  +  f  .c—  pig  —weed  X  l.Op'"™ 

V— pig 

(l.Op^-1) 

3.  The  value  of  an  ideal  forest  in  which  all  age  classes  are  present,  which 

is  conservatively  managed,  close  to  a  ready  market  (so  that  in  every 
year  of  the  future  there  may  be  obtained  a  yield  from  a  thinning  in 
a  woodlot  "a",  ''b",  "c"  years  old  and  also  a  final  yield  diminished 
by  reforestation  expenses,  whilst  the  expense  of  administration  is  an- 
nually "v"  for  the  entire  forest)  amounts  to 

thna  +thnb  +thnc  +  (f.c— pltg)  —  v 

in  which 

O.Op 

thn  equals  thinnings 
p  "      rate  per  cent. 

f.c.       "      final  cut 
pltg      "      planting. 


24  FOREST  FINANCE 

PARAGRAPH  X.— SALE  VALUE  OF   WOODLANDS 
IN  U.  S. 

It  is  customary  to  buy  timberland  merely  at  the  price  of  the  stumpage 
standing  thereon.     The  purchaser  neglects: 

C  /  1)  that  he  can  not  cut  all  of  the  timber  at  once;  and  such  parts,  as 

■5  \  he  cuts  only  after  some  years,  should  not  be  assessed  at  full  value ; 

*"  j  2)  that  taxes,  etc.,  accrue,  whilst  the  timber  is  cut  gradually; 

>  \  3)  that  an  expense  for  legal  and  timber  investigations  must  be  covered; 

g,  /  4)  that  timber  values  might  be  destroyed  by  fire; 

K  I  6)  that  there  is  danger  of  fool-legislation  against  alien  corporationg. 

a)  that  soil  has  value; 

b)  that  stumpage  prices  (and  merchantability,  hence  volume)  will 
increase ; 

c)  that  there  is  a  second  growth  already  at  hand; 

d)  that  local  means  of  transportation  increase; 

e)  that  taxes  might  be  decreased,  and  that  protective  legislation  will 
come; 

f)  that  freight  rates  decrease; 

g)  that  population  increases,  also  demand; 
h)      that  new  uses  are  found  for  wood ; 
i)       that  investments  in  forestry  are  remarkably  safe,  compared  with 

stocks,  bonds,  etc. 

j)  that  the  agricultural  value  of  the  soil  increases,  absolute  forest  soil 
becoming  absolute  farm  soil,  as  the  years  go  by; 

k)  that  forest  pasture,  chase,  minerals  (rock,  clay),  waters  and  water- 
powers  promise  an  increasing  revenue. 

PARAGRAPH  XI.— GAUGING  THE  MERITS  OF  AN 
INVESTMENT. 

The  Success  of  a  business  (in  farms,  mines,  forestry)  is  evidenced  by  its 
net  gains. 

Expenses  and  yields  can  be  compared  either  by  forming  their  difference 
which  comparison  shows  an  "entrepreneur's"  gain  or  loss;  or  by  forming 
theu-  ratio  which  method  shows  the  actual  dividend  obtained  from  the  business. 
I. — Entrepreneur's  gain  and  loss. 

Influencing  factors  are: — 

a.  Lapse  of  time. 

b.  Constellation  of  economic  conditions. 

c.  Personal  foresight. 

d.  Rate  of  interest  introduced  into  the  calculation. 

An  undertaker's  gain  may  be  figured  out  retrospectively  or  prospectively. 
An  undertaker's  gain  is  fictitious  until,  the  property  changing  hands,  it 
can  be  demonstrated  to  be  a  fact. 


FOREST  FINANCE  28 

The  undertaker's  gain  or  loss  disappears  when  the  financier  introduces 
a  rate  of  interest  at  which  the  discounted  expense  equals  the  discounted  yields. 

n. — The  forest  dividends  show  what  actual  rate  of  interest  the  owner  has 
made  in  the  past  or  may  earn  in  the  future  on  his  investments.  The 
actual  rate  of  interest  introduced  in  the  financial  equation  causes  any 
undertaker's  gain  to  vanish. 

The  forest  dividend  is  deeply  influenced  by  the  price  increment  of  trees 
(improved  means  of  transportation;  enlarged  markets,  etc.) 

In  the  forest,  it  is  difficult  to  distinguish  between  actual  revenue  drawn 
from  the  forest  and  capital  withdrawn,  since  the  trees  are  capital  as  well  as 
product.  In  conservative  forestry,  careful  stock  taking  is  required  period- 
ically, so  as  to  show  the  actual  status  of  the  investment. 

PARAGRAPH  XII.— MATURITY  OF  TREES. 

I. — In  the  botanical  sense,  wood  fiber  is  mature  almost  after  the  conception 
of  the  cell. 

A  tree  3  inches  in  diameter  is  physiologically  just  as  mature  as  a  tree 
3  feet  in  diameter. 
The  highest  stage  of  botanical  maturity  is  the  so-called  heartwood. 

II. — From  the  people's  standpoint,  timber  must  be  considered  mature  at  a 
time  at  which  it  is  best  adapted  to  general  usage  in  the  wood  consuming 
industries.  The  older  the  tree  gets,  the  larger  is,  on  the  whole,  its  diver- 
sity of  utility.  The  rotation  best  adapted  to  supply  the  industries  of  a 
country  is  called  the  "technical  rotation". 

in. — The  sylviculturist  regenerating  the  forest  from  self-sown  seed  cannot 
select  a  rotation  which  does  not  allow  the  trees  to  profusely  propagate 
their  kind.  In  coppice  woods,  since  the  sprouting  capacity  decreases 
with  increasing  diameter,  the  rotation  must  be  so  low  as  to  allow  of 
luxuriant  production  (sylvicultural  rotation). 

rV. — From  the  financial  standpoint,  trees  or  forests  must  be  considered  mature 
when  the  net  true  interest  obtained  from  them  ceases  to  bear  a  sufficient 
ratio  to  the  sale  value  of  such  trees  or  forests. 

Wherever  the  woods  are  stocked  with  even  aged  and  even  sized  trees, 
all  of  the  trees  reach  maturity  at  or  about  at  the  same  time. 
The  primeval  woods  of  America  do  not  exhibit,  usually,  such  even  aged 
conditions.     The  American  forester  had  better  speak  of  the  maturity  of  trees 
than  of  the  maturity  of  forests. 

Factors  influencing  the  maturity  of  trees  in  America  are,  pre-eminently : — 

a.     The  price  increment,  which,  in  the  case  of  large  trees,  far  exceeds 

the  volume  increment  and  value  increment.     Stem  analyses  and 

volume  tables  are  of  little  value,  consequently,  for  the  financial 

diagnosis  of  primeval  trees. 


26  FOREST  FINANCE 

b.  Means  or  arteries  of  transportation  and  the  permanency  of  their  char- 

acter. Where  the  means  of  transportation  are  considered  as  a 
permanent  investment  and  not  as  a  temporary  expense  to  be  re- 
imbursed by  current  operations,  a  higher  age  of  maturity  results 
naturally. 

c.  In  many  cases  the  taxes  per  acre  are  not  or  are  scarcely  influenced 

by  the  severity  of  the  cut.  Here  it  is  irrelevant,  from  the  tax 
payer's  standpoint,  whether  he  proceed  to  log  certain  sizes  or  kinds 
of  trees  or  not.  Where,  on  the  other  hand,  taxes  are  changed  ac- 
cording to  the  stumpage  found  per  acre,  the  standing  tree  must  be 
charged  with  that  much  of  the  tax  per  acre  as  corresponds  with 
its  individual  contents.  Take,  e.  g.,  a  forest  of  white  pine  contain- 
ing 5,000  ft.  per  acre  consisting  of  12  trees  averaging  400  ft.  b. 
m.,  taxed  at  30  cts.  per  acre.     The  soil  has  little  value.    A  tree  con- 

.30  X  400 

taining  400  ft.b.m.  must  annually  defray    =.024,  which 

6000 
expense  of  .024  must  be  charged  against  the  tree  and  must  be  de- 
frayed from  the  annual  increase,  if  any,  of  the  value  of  the  tree. 

d.  Trees  acting  as  mother  trees  propagating  their  kind  should  be  credited 

with  the  prospective  value  of  the  progeny  produced  by  them,  on 
an  average.  On  the  other  hand,  trees  acting  like  weeds  and  re- 
tarding the  growth  of  a  younger  progeny  of  seedlings  and  saplings 
beneath  them  must  be  charged  with  the  loss  of  prospective  incre- 
ment incurred  by  such  second  growth. 

e.  Since  protective  and  administrative  expenses  are  governed  more  by 

area  than  by  the  density  of  the  stands,  it  is  necessary  in  rare  cases 
only  to  charge  a  pro  rata  of  the  protective  and  administrative  ex- 
penses against  the  individual  tree.  These  expenses  incumber  the 
soil  like  prescriptive  rights. 

f.  The  question  of  maturity  is  a  question  to  be  answered  in  the  first 

and  last  instance  by  the  owner  who  is  governed  by  his  personal 
attitude  regarding  the  rate  of  interest  obtainable  from  his  invest- 
ment; by  the  prospects  of  price  increment  as  they  appear  to  him 
and  by  personal  moments  like  the  lack  of  cash  to  defray  running 
expenses,    mortgages,    etc.;    chance    of    remunerative    investment 
elsewhere;  desire  to  distribute  risks;  tastes  and  predilections. 
Trees  of  defective  character  infested  by  insects  or  fungi  have  reached 
maturity,    generally   speaking,   since   the  spread  of   the   disease   checks  their 
financial  increment,  and  may  cause  the  increment  to  be  negative. 
V. In  Europe  the  following  number  of  years  denote,  on  an  average,  the  ma- 
turity of  timber:  pine  100  yrs.;  spruce  90  yrs.;  fir  120  yrs.;  beech  120 
yrs.;  oak  160  yrs.;  oak  coppice  18  yrs.;  willows  1  and  2  yrs. 
In  America,  naturally,  fixed  rotations  have  not  been  adopted,  since  the 
cutting  takes  place,  usually,  in  the  primeval  woods.     In  Virginia,  a  second 
and  third  growth  of  pine  is  cut  under  a  rotation  of  about  60  years.    Catalpa 


FOREST  FINANCE  2T 

is  coppiced  under  a  rotation  of  about  10  years.  The  very  prime  trees,  notably 
hardwoods,  of  a  primeval  wood  are  immature  from  a  financial  standpoint, 
if  the  owner  believes  that  the  greatest  advance  in  prices  will  come  to  them, 
such  giants  getting  rare  and  more  rare,  year  by  year. 

In  many  cases,  the  price  of  inferior  stumpage  does  not  promise  to  rise  as 
much  as  the  price  of  prime  stumpage.  On  the  other  hand,  in  many  a  case, 
the  indicating  percentage  of  trees  promising  a  large  percentage  of  "cull  lum- 
ber" is  manifestly  superior  to  that  of  trees  containing  a  large  percentage  of 
"fas  lumber". 

In  Europe,  the  question  of  maturity  is  largely  a  question  of  age  or  (which 
is  almost  the  same)  of  diameter.  In  America,  on  the  other  hand,  the  question 
is  one  of  conditions — condition  of  transportation,  danger  from  fire,  condition 
of  health,  the  chances  for  their  improvement  or  deterioration.  Thus,  a  diam- 
eter limit  or  age  limit  can  scarcely  denote  maturity.  The  American  forester 
in  charge  of  large  districts  is  confronted  many  a  time  with  the  necessity  of 
treating  individual  trees  according  to  their  financial  merits,  whilst  his  Euro- 
pean colleague  in  charge  of  small  ranges  has  to  deal  with  even  aged  aggre- 
gates resulting  from  second  growths. 

VI. — The  term  "indicating  percentage"  denotes  the  current  dividend  obtain- 
able from  a  tree  or  woodlot.     This  percentage  indicates  the  maturity  of  a 

tree  or  of  a  woodlot. 

A  tree  or  woodlot  is  mature  and  should  be  removed  when  it  ceases  to  yield 
(latently,  of  course)  the  dividend  desired  by  the  owner. 

The  owner  or  investor  discards  an  investment  in  forestry  as  well  as  in 
stock  when  the  dividend  seems  to  fall  below  the  limit  obtainable  by  him  in 
other  enterprises  of  similar  safety.  If  he  discards  at  the  right  time,  he  will 
make  money;  and  otherwise  not. 

In  the  following  remarks,  the  indicating  percentage  is  called  "x";  the 
forest  percentage  denoting  the  "limit"  just  mentioned  is  called  "p". 

Previous  to  maturity,  "x"  is  larger  than  "p";  at  maturity,  "x"  equals 
"p";  after  maturity  "x"  is  smaller  than  "p". 

The  indicating  percentage  of  a  woodlot,  for  a  period  of  10  years,  is  as 
follows,  if  the  stumpage  is  now  worth  "S.S."  dollars;  if  it  is  worth,  after  ten 
years,  "S-S^g";  if  the  cleared  soil  is  worth  "C"  dollars;  if  administration  and 
taxes  are  "v"  dollars  per  annum,  forming  an  administrative  capital  "V": — 

(SS  +  C  +  V)  1.0x10  -  SSio  +  C  +  V  or 

(1.0x10—1) 

(SS  +  C)  1.0x10 +v -C+SSio 

O.Ox 

According  to  Krafft,  the  indicating  percentage  had  better  be  considered 
as  a  dividend  on  stumpage  merely  v/hilst  the  soil  and  the  administrative  cap- 
ital should  yield  the  forest  dividend  required  by  the  owner. 

Krafft's  "x"  is  more  sensitive  than  the  "x"  commonly  applied  since  it 
bears  a  ratio  to  part  of  the  investment  only.  Krafft's  "x"  is  found asfollows: — 
SS  X  1.0x10  + (C+V)  1.0plO=  SSio  +  C+V 


as  FOREST  FINANCE 

In  conservative  logging  when  a  portion  only  of  the  trees  are  removed  from 
•very  acre,  the  indicating  percentage  had  best  be  considered  as  a  tree  dividend. 

Whether  and  how  much  of  the  taxes  and  administrative  expense  (e) 
should  be  charged  to  the  tree,  depends  upon  the  local  circumstances.  Trees 
occupying  soil  and  preventing,  by  their  presence,  a  second  growth  from  de- 
veloping, must  be  charged  with  the  interest  on  the  value  of  the  soil  thus  oc- 
cupied. 

On  the  other  hand,  trees  acting  as  mother  trees  must  be  credited  with 
the  value  of  the  progeny  resulting  from  their  presence. 

The  tree  indicating  percentage  might  be  expressed,  adopting  Kraflft's 
method,  as  follows : 

(l.Opn— 1) 

To  X   1.0x°+e +  (soil)  1.0p°=Tn  +  soil  +  value   of    progeny 

O.Op 
in  which  "Tq"  equals  the  tree  value  now.    Where  the  forest  stocks  on  agricul- 
tural soil,  all  trees  unable  to  defray  the  interest  on  such  valuable  soil,  appear 
to  be  mature,  or  hypermature. 

VII. — The  forester  making  a  working  plan  for  pine  and  spruce  woods  is  usually 
confronted  by  the  question  of  the  best  diameter  limit.  The  plan  advises 
the  owner  as  to  the  limit  yielding  the  highest  entrepreneur's  gain  or  the 
highest  forest  dividend. 

The  heavier  the  present  cut,  the  smaller  is  the  investment  left,  whilst  the 
protecting  expenses  remain  the  same.  On  the  face  of  it,  it  seems  unwise  to 
cut  clear  without  considering  the  financial  prospects  of  trees  which  might  be 
left  on  the  ground,  having  10",  12",  14",  etc.  in  diameter.  Obviously,  the 
logging  expenses  per  M  feet  b.  m.,  are  smaller  in  the  case  of  heavy  cutting, 
than  in  the  case  of  light  cutting,  particularly  so  when  the  logger  must  avoid 
any  damage  to  the  trees  left  standing. 

Again,  obviously,  the  longer  the  period  of  waiting  for  a  second  cut,  the 
less  are  the  chances  for  a  good  return  from  conservative  logging. 

The  diameter  limit  might  be  tested  either  with  the  help  of  the  indicating 
percentage  or  by  the  method  of  the  entrepreneur's  gain. 


INTEREST  TABLES 


(EXPLANATORY) 

Column  I  indicates  the  number  of  years. 

Column    II    gives   the  present   value   of  $1.00  due   at   the  end  of  the 
number  of  years  indicated  in  column  I. 

Column  III  gives  the  present  value  of  $1.00  per  annum  due  every  year 
during  the  period  of  years  indicated  in  colimm  I. 

Column  IV  gives  the  aft-value  of  $1.00  left  invested  for  the  number  of 
years  indicated  in  column  I. 

Column    V    gives    the    aft-value    of    SI. 00    payable    annually    and    left 
invested  for  the  number  of  years  indicated  in  column  I. 


80 


^  PER  CENT. 


I 

II 

III 

iiii 

V 

1 

.9950 

.9950 

1.0050 

1.0000 

2 

.9901 

1.9851 

1.0100 

2.0050 

3 

.9851 

2.9702 

1.0151 

3.0150 

4 

.9802 

3.9505 

1.0202 

4.0301 

5 

.9754 

4.9259 

1.0253 

5.0503 

6 

.9705 

5.8964 

1.0304 

6.0755 

7 

.9657 

6.8621 

1.0355 

7.1059 

8 

.9609 

7.8230 

1.0407 

8.1414 

9 

.9561 

8.7791 

1.0459 

9.1821 

10- 

....9513.. 

9.7304-. 

1.0511.. 

10.2280 

11 

.9466 

10.6770 

1.0564 

11.2792 

12 

.9419 

11.6189 

1.0617 

12.3356 

13 

.9372 

12.5562 

1.0670 

13.3972 

14 

.9326 

13.4887 

1.0723 

14.4642 

15 

.9279 

14.4166 

1.0777 

15.5365 

16 

.9233 

15.3399 

1.0831 

16.6142 

17 

.9187 

16.2586 

1.0885 

17.6973 

18 

.9141 

17.1728 

1.0939 

18.7858 

19 

.9096 

18.0824 

1.0994 

19.8797 

20 

.9051 

18  9874  - 

__1.1049. 

20.9791 

21 

.9006 

19.8880 

1.1104 

22.0840 

22 

.8961 

20.7841 

1.1160 

23.1944 

23 

.8916 

' 21 . 6756 

1.1216 

24.3104 

24 

.8872 

22.5629 

1 . 1272 

25.4320 

25 

.8828 

23.4456 

1 . 1328 

26.5591 

26 

.8784 

124.3240 

1 . 1385 

27.6919 

27 

.8740 

■^  25 .  1980 

1.1442 

28.8304 

28 

.8697 

^26.0677 

1 . 1499 

29.9745 

29 

.8653 

iT  26. 9330 

1 . 1556 

31.1244 

30 

8610 

___27.7941-- 

-  1  1614 

32.2800 

3l' 

.8567 

28.6508 

1 . 1672 

33.4414 

32 

.8525 

29.5033 

1 . 1730 

34.6086 

33 

.8482 

30.3515 

1.1789 

35.7817 

34 

.8440 

30.1955 

1 . 1848 

36.9606 

35 

.8398 

32.0354 

1 . 1907 

38.1454 

36 

.8356 

32.8710 

1 . 1967 

39.3361 

37 

.8315 

33.7025 

1.2027 

40.5328 

38 

.8274 

34.5299 

1.2087 

41.7354 

39 

.8232 

35.3531 

1.2147 

42.9441 

40 

8191 

36  1722 

1  2208 

.44.1588 

41 

.8151 

36.9873 

1.2269 

45.3796 

42 

.8110 

37.7983 

1.2330 

46.6065 

43 

.8070 

38.6053 

1.2392 

47.8306 

44 

.8030 

39.4082 

1.2454 

49.0788 

45 

.7990 

40.2072 

1.2516 

50.3242 

46 

.7950 

41.0022 

1.2579 

51.5758 

47 

.7910 

41.7932 

1.2642 

52.8337 

48 

.7871 

42.5803 

1.2705 

54.0978 

49 

.7832 

43.3635 

1.2768 

55.3683 

60 

....7793_. 

...44.1428.. 

..._1.2832._ 

.....56.6452 

55 

.7601 

47.9782 

1.3156 

63.1200 

60 

.7414 

51.7020 

1.3488 

69.7600 

65 

.7231 

55.2764 

1.3829 

76.5800 

70 

.7053 

58.9364 

1.4178 

83.5600 

75 

.6879 

62.4745 

1.4536 

90.7200 

80 

.6710 

65.7988 

1.4903 

98.0600 

85 

.6545 

69.1099 

1.5280 

105.6000 

90 

.6383 

72.3268 

1.5665 

113.3000 

95 

.6226 

75.4747 

1.6061 

121.2200 

100.. 

..-.6073.- 

...78.5449.. 

....1.6467.. 

129.3400 

105 

.5923 

81.5306 

1.6882 

137.6400 

110 

.5777 

84.4531 

1.7309 

146.1800 

115 

.5635 

87.2985 

1.7746 

154.9200 

120 

.5496 

90.0736 

1.8194 

163.8800 

1  PER  CI 

:nt. 

I 

n 

1 

mi 

V 

1 

.9901 

.9901 

1.0100 

1.0000 

2 

.9803 

1.9704 

1.0201 

2.0100 

3 

.9706 

2.9410 

1.0303 

3.0301 

4 

.9610 

3.9020 

1.0406 

4.0604 

5 

.9515 

4.8534 

1.0510 

5.1010 

6 

.9420 

5.7955 

1.0615 

6.1520 

7 

.9327 

6.7282 

1.0721 

7.2135 

8 

.9235 

7.6517 

1.0829 

8.2857 

9 

.9143 

8.5660 

1.0937 

9.3685 

10 

.9053__ 

9.4713.. 

1.1046.. 

10.4622 

11 

.8963 

10.3676 

1.1157 

11.5668 

12 

.8874 

11.2551 

1.1268 

12.6825 

13 

.8787 

12.1337 

1.1381 

13.8093 

14 

.8700 

13.0037 

1 . 1495 

14.9474 

15 

.8613 

13.8651  1 

1.1610 

16.0969 

16 

.8528 

14.7179  i 

1 . 1726 

17.2579 

17 

.8444 

15.5622 

1 . 1843 

18.4304 

18 

.8360 

16.3983 

1.1961 

19.6147 

19 

.8277 

17.2260 

1.2081 

20.8109 

20 

.8195.. 
.8114 

.18.0456.. 
18.8570 

1.2202 

.22.0190 

21" 

1.2324 

23.2392 

22 

.8034 

19.6604 

1.2447 

24.4716 

23 

.7954 

20.4558 

1.2572 

25.7163 

24 

.7876 

21.2434 

1.2697 

26.9735 

25 

.7798 

22.0232 

1.2824 

28.2432 

26 

.7720 

22.7952 

1.2953 

29.5256 

27 

.7644 

23.5596 

1.3082 

30.8209 

28 

.7568 

24.3164 

1.3213 

32.1291 

29 

7493 

25.0658 

1.3345 

33.4504 

30 

7419 

.25.8077.. 

1.3478.. 
1.3613 

.34.7849 

31 

7346 

■  26.5423 

36.1327 

32 

7273 

27.2696 

1.3749 

37.4941 

33 

.7201 

27.9897 

1.3887 

38.8690 

34 

7130 

28.7027 

1.4026 

40.2577 

35 

7059 

29.4086 

1.4166 

41.6603 

36 

6989 

30.1075 

1.4308 

43.0769 

37 

6920 

30.7995 

1.4451 

44.5076 

38 

6852 

31.4847 

1.4595 

45.9527 

39 

6784 

32.1630 

1.4741 

47.4123 

40 

6717 
"■  6650 

32. 8347.. 
"'33.4997 

1.4889 

.48.8864 

41" 

1.5038 

50.3752 

42 

6584 

34.1581 

1.5188 

51.8790 

43 

6519 

34.8100 

1.5340 

53.3978 

44 

6454 

1   35.4554 

1.5493 

54.9318 

45 

6391 

36.0945 

1.5648 

56.4811 

46 

6327 

i   36.7272 

1.5805 

58.0459 

47 

6265 

i   37.3537 

1.5963 

59.6263 

48 

6203 

1   37.9740 

:    1.6122 

61.2226 

49 

.6141 

1   38.5881 

1    1.6283 

j     62.8348 

60 

6080 

!   39.1961__ 

!.... 1.6446.. 

1 64.4632 

55 

"".5786 

42.1430 

1.7284 

1     72.8400 

60 

.5505 

44.9521 

1.8166 

81.6600 

65 

.5238 

47.6247 

1.9093 

90.9300 

70 

4983 

50.1644 

2.0066 

!    100.6600 

75 

.4742 

52.5841 

2.1090 

110.9000 

80 

.4500 

54.8858 

2.2166 

121.6600 

85 

.4292 

57.0742 

2.3296 

132.9600 

90 

.4084 

59 . 1750 

2.4485 

144.8500 

95 

.3886 

61 . 1394 

2.5733 

157.3300 

100_. 

3697- 

._.63.0259.- 

....2.7046.. 

170.4600 

105 

.3518 

64.8197 

2.8425 

184.2500 

110 

.3347 

66.5272 

2.9875 

198.7500 

115 

.3185 

68.1518 

3 . 1399 

213.9900 

120 

.3030 

1   69.6979 

3.3001 

230.0100 

31 


32 


1}4  PER  CENT. 


I   1 

II 

III 

iiii 

V 

1 

.9852 

.9852 

1.0150 

1.0000 

2 

.9707 

1.9559 

1.0302 

1.0150 

3 

.9563 

2.9122 

1.0457 

3.0452 

4 

.9422 

3.8544 

1.0614 

4.0909 

6 

.9283 

4.7826 

1.0773 

5.1523 

6 

.9145 

5.6972 

1.0934 

6.2290 

7 

.9010 

6.5982 

1 . 1098 

7.3230 

8 

.8877 

7.4859 

1 . 1265 

8.4328 

9 

.8746 

8.3605 

1.1434 

9.5593 

10.. 

....8617__ 

9.2222.. 

1.1605.. 

10.9027 

11 

.8489 

10.0711 

1 . 1779 

11.8633 

12 

.8364 

10.9075 

1 . 1959 

13.0412 

13 

.8240 

11.7315 

1.2130 

14.2368 

14 

.8118 

12.5434 

1.2318 

15.4504 

15 

.7999 

13.3432 

1.2502 

16.6821 

16 

.7880 

14.1313 

1.2690 

17.9324 

17 

.7764 

14.9076 

1.2880 

19.2014 

18 

.7649 

15.6726 

1.3073 

20.4894 

19 

.7536 

16.4262 

1.3270 

21.7967 

20 

7425.. 

.7315 

...17.1686.. 
17.9001 

1.3469  . 

23.1237 

21 

1.3671 

24.4705 

22 

.7207 

18.6208 

1 . 3876 

25.8376 

23 

.7100 

19.3309 

1.4084 

27.2251 

24 

.6995 

20.0304 

1.4295 

28.6335 

25 

.6892 

20.7196 

1.4509 

30.0630 

26 

.6790 

21.3986 

1.4727 

31.5140 

27 

.6690 

22.0676 

1.4948 

32.9867 

28 

.6591 

22.7267 

1.5172 

34.4815 

29 

.6494 

23.3761 

1.5400 

35.9987 

30 

6398.- 

.6303 

...24.0158.. 
24.6461 

1.5631  . 

37.5387 

31 

1.5865 

39.1018 

32 

.6210 

25.2671 

1.6103 

40.6883 

33 

.6118 

25.8790 

1.6345 

42.2986 

34 

.6028 

26.4817 

1.6590 

43.9331 

35 

.5939 

27.0756 

1.6839 

45.5921 

36 

.5851 

27.6607 

1.7091 

47.2760 

37 

.5764 

28.2371 

1.7348 

48.9851 

38 

.5679 

28.8051 

1.7608 

50.7199 

39 

.5595 

29.3646 

1.7872 

52.4807 

40 

....5513.. 
.5431 

...29.9158.. 
30.4590 

1.8140.. 

54.2679 

41 

1.8412 

56.0819 

42 

.5351 

30.9940 

1.8688 

57.9231 

43 

.5272 

31.5212 

1.8969 

59.7920 

44 

.5194 

32.0406 

1.9253 

61.6889 

45 

.5117 

32.5523 

1.9542 

63.6142 

46 

.5042 

33.0565 

1.9835 

65.5684 

47 

.4967 

33.5532 

2.0133 

67.5519 

48 

.4894 

34.0426 

2.0435 

69.5652 

49 

.4821 

34.5247 

2.0741 

71.6087 

50 

4750.. 

.4409 

34.9997  . 

..  2.1052.. 

73.6828 

65 

37.2715 

2.2679 

84.5296 

60 

.4093 

39.3803 

2.4432 

96.2147 

65 

.3799 

41.3373 

2.6320 

108.8000 

70 

.3527 

43 . 1549 

2.8355 

122.3640 

75 

.3274 

44.8409 

3.0546 

136.9670 

80 

.3039 

46.4073 

3.2907 

152.7110 

85 

.2821 

47.8603 

3.5450 

169.6600 

90 

.2618 

49.2099 

3.8189 

187.9300 

95 

.2431 

50.4618 

4.1141 

207.6000 

100.. 

2256.. 

...51.6247.. 

....4.4320_. 

228.8030 

105 

.2094 

52.7036 

4.7746 

251.6330 

110 

.1944 

53.7055 

5.1436 

276.2380 

115 

.1805 

54.6351 

5.5411 

302.7330 

120 

.1675 

55.4985 

5.9693 

331.2880 

2  PER  CENT. 


33 


I 

II 

III 

iiii 

V 

1 

.9804 

.9804 

1.0200 

1.0000 

2 

.9612 

1.9416 

1.0404 

2.0200 

3 

.9423 

2.8839 

1.0612 

3.0604 

4 

.9238 

3.8077 

1.0824 

4.1216 

5 

.9057 

4.7135 

1.1041 

5.2040 

6 

.8880 

5.6014 

1 . 1262 

6.3081 

7 

.8706 

6.4720 

1.1487 

7.4343 

8 

.8535 

7.3255 

1.1717 

8.5830 

9 

.8368 

8.1622 

1.1951 

9.7546 

10__ 

..-.8203.. 
.8043 

8. 9826.. 

9.7868 

.  1.2190 

10  9497 

11 

1.2434 

12.1687 

12 

.7885 

10.5753 

1.2682 

13.4121 

13 

.7730 

11.3484 

1.2936 

14.6803 

14 

.7579 

12.1062 

1.3195 

15.9739 

16 

.7430 

12.8493 

1.3459 

17.2934 

16 

.7284 

13.5777 

1 . 3728 

18.6393 

17 

.7142 

14.2919 

1.4002 

20.0121 

18 

.7002 

14.9920 

1.4282 

21.4123 

19 

.6864 

15.6785 

1.4568 

22.8406 

20._ 

__-.6730.. 
.6598 

__.16.3514.. 
17.0112 

..1.4859 

24  2974 

21 

1.5157 

25.7833 

22 

.6468 

17.6580 

1.5460 

27.2990 

23 

.6342 

18.2922 

1.5769 

28.8450 

24 

.6217 

18.9139 

1.6084 

30.4219 

26 

.6095 

19.5235 

1.6406 

32.0303 

26 

.5976 

20.1210 

1.6734 

33.6709 

27 

.5859 

20.7069 

1.7069 

35.3443 

28 

.5744 

21.2813 

1.7410 

37.0512 

29 

.5631 

21.8444 

1.7758 

38.7922 

30.  _ 

__-.5521.. 
.5412 

-  .22.3965. 
22.9377 

.-.-1.8114__ 

40.5681 

31 

1.8476 

42.3794 

32 

.5306 

23.4683 

1.8845 

44.2270 

33 

.5202 

23.9886 

1.9222 

46.1116 

34 

.5100 

24.4986 

1.9607 

48.0338 

36 

.5000 

24.9986 

1.9999 

49.9945 

36 

.4902 

25.4888 

2.0399 

51.9944 

37 

.4806 

25.9695 

2.0807 

54.0343 

38 

.4712 

26.4406 

2.1223 

56.1149 

39 

.4619 

26.9026 

2.1647 

58.2372 

40.. 

4529.. 

.4440 

-.27.3555 

....2.2080.. 

.60.4020 

41 

27.7995 

2.2522 

62.6100 

42 

.4353 

28.2348 

2.2972 

64.8622 

43 

.4268 

28.6616 

2.3432 

67.1595 

44 

.4184 

29.0800 

2.3901 

69.5027 

46 

.4102 

29.4902 

2.4379 

71.8927 

46 

.4022 

29.8923 

2.4866 

74.3306 

47 

.3943 

30.2866 

2.5363 

76.8172 

48 

.3865 

30.6731 

2.5871 

79.3535 

49 

.3790 

31.0521 

2.6388 

81.9406 

60.. 

3715.. 

.3365 

...31.4236.. 
33.1748 

....2.6916.. 

_  .84.5794 

66 

2.9717 

98.5865 

60 

.3048 

34.7609 

3.2810 

114.0520 

66 

.2760 

36.1973 

3.6225 

131  .1250 

70 

.2500 

37.4986 

3.9995 

149.9780 

75 

.2265 

38.6763 

4.4158 

170.7900 

80 

.2051 

39.7445 

4.8754 

193.7720 

85 

.1858 

40.7111 

5.3828 

219.1400 

90 

.1683 

41.5869 

5.9431 

247.1570 

95 

.1524 

42.3800 

6.5617 

278.0850 

100.. 

....1380.. 

...43.0984.. 

....7.2446.. 

312.2320 

105 

.1250 

43.7489 

7.9987 

349.9300 

110 

.1132 

44.3382 

8.8312 

391.5590 

116 

.1026 

44.8719 

9.7503 

437.5150 

120 

.0929 

45.3554 

10.7652 

488.2580 

34 


21^  PER  CENT. 


I 

ir 

III 

iiii 

V 

1 

.9756 

.9756 

1.0250 

1.0000 

2 

.9518 

1.9274 

1.0506 

2.0250 

3 

.9286 

2.8560 

1.0769 

3.0756 

4 

.9060 

3.7620 

1 . 1038 

4.1525 

6 

.8839 

4.6458 

1.1314 

5.2563 

6 

.8623 

5.5081 

1 . 1597 

6.3877 

7 

.8413 

6.3494 

1 . 1887 

7.5474 

8 

.8207 

7.1701 

1.2184 

8.7361 

9 

.8007 

7.9709 

1.2489 

9.9545 

10 

.7812 

..8.7521._ 

1.2801.. 

11.2034 

11 

.7621 

9.5142 

1.3121 

12.4835 

12 

.7436 

10.2578 

1.3449 

13.7956 

13 

.7254 

10.9832 

1.3785 

15.1404 

14 

.7077 

11.6909 

1.4130 

16.5190 

15 

.6905 

12.3814 

1.4483 

17,9319 

16 

.6736 

13.0550 

1.4845 

19.3802 

17 

.6572 

13.7122 

1.5216 

20.8647 

18 

.6412 

14  .3534 

1.5597 

22.3863 

19 

.6255 

14.9789 

1.5987 

23.9460 

20 

._..6103.. 
.5954 

15.5892_. 
16.1845 

..1.6386.. 

25.5447 

21 

1.6796 

27.1833 

22 

.5809 

16.7654 

1.7216 

28.8629 

23 

.5667 

17.3321 

1.7646 

30.5844 

24 

.5529 

17.8850 

1.80S7 

32.3490 

26 

.5394 

18.4244 

1.8539 

34.1578 

28 

.5262 

18.9506 

1.9003 

36.0117 

27 

.5134 

19.4640 

1.9478 

37.9120 

28 

.5009 

19.9649 

1.9965 

39.8598 

29 

.4887 

20.4535 

2.0464 

41.8563 

30 

.4767  . 

20.9303.. 
21.3954 

..2.0976.. 

43.9027 

31 

.4651 

2 . 1500 

46.0003 

32 

.4538 

21.8492 

2.2038 

48.1503 

33 

.4427 

22.2919 

2.2589 

50.3540 

34 

.4319 

22.7238 

2.3153 

52.6129 

35 

.4214 

23.1452 

2.3732 

54.9282 

36 

.4111 

23.5563 

2.4325 

57.3014 

37 

.4011 

23.9573 

2.4933 

59.7339 

38 

.3913 

24.3486 

2.5557 

62.2273 

39 

.3817 

24.7303 

2.6196 

64.7830 

40 

._..3724__ 
.3633 

25.1028.. 
25.4661 

2.6851 

67 . 4026 

4l" 

2.7522 

70.0876 

42 

.3545 

25.8206 

2.8210 

72.8398 

43 

.3458 

26.1664 

2.8915 

75.6608 

44 

.3374 

26.5038 

2.9638 

78.5523 

45 

.3292 

26.8330 

3.0379 

81.5161 

46 

.3211 

27.1542 

3.1139 

84.5540 

47 

.3133 

27.4675 

3.1917 

87.6679 

48 

.3057 

27.7732 

3.2715 

90.8596 

49 

.2982 

28.0714 

3.3533 

94.1311 

50 

.2909.. 

.28.3623.. 

3.4371.. 

97.4843 

66 

.2571 

29.7140 

3.8888 

115.551 

60 

.2273 

30.9087 

4.3998 

135.992 

66 

.2009 

31.963 

4.9780 

159 . 120 

70 

.1775 

32.898 

5.6321 

185.284 

75 

.1569 

33.645 

6.3722 

214.888 

80 

.1387 

34.452 

7.2096 

248.383 

85 

.1226 

35.096 

8.1570 

286.280 

90 

.1084 

35.666 

9.2289 

329 . 154 

95 

.0958 

36.171. 

10.4416 

377.664 

100.  _ 

....0846.. 

...36. 614... 

...11.8137.. 

-...432.549 

105 

.0748 

37.007 

13.3661 

494.644 

110 

.0661 

37.355 

15.1226 

564.902 

115 

.0584 

37.664 

17 . 1098 

644.392 

120 

.0517 

37.934 

19.3581 

734.326 

3  PER  CENT. 


86 


I 

II 

III 

IV 

V 

1 

.9709 

.9709 

1.0300 

1.0000 

2 

.9426 

1.9135 

1.0609 

2.0300 

3 

.9151 

2.8286 

1.0927 

3.0909 

4 

.8885 

3.7171 

1.1255 

4 . 1836 

6 

.8626 

4.5797 

1 . 1593 

5.3091 

6 

.8375 

5.4172 

1.1941 

6.4684 

7 

.8131 

6.2303 

1.2299 

7.6625 

8 

.7894 

7.0197 

1.2668 

8.8923 

9 

.7664 

7.7861 

1 . 3048 

10.1591 

10 

7441.. 

8  5302  ' 

-1  3439 

11 .4639 

11 

.7224 

9^2526 

1.3842 

12 '8075 

12 

.7014 

9.9540 

1.4258 

14.1920 

13 

.6810 

10.6350 

1.4685 

15.6178 

14 

.6611 

11.2961 

1.5126 

17.0863 

15 

.6419 

11.9379 

1.5580 

18.5989 

16 

.6232 

12.5611 

1.6047 

20.1569 

17 

.6050 

13.1661 

1.6528 

21.7616 

18 

.5874 

13.7535 

1.7024 

23.4144 

19 

.5703 

14.3238 

1.7535 

25.1169 

20-- 

5537__ 

14.S775-- 

1  8061 

26  8704 

21 

.5375 

15^4150 

1^8603 

28^6765 

22 

.5219 

15.9369 

1.9161 

30.5368 

23 

.5067 

16.4436 

1.9736 

32.4529 

24 

.4919 

16.9325 

2.0328 

34.4265 

25 

.4776 

17.4131 

2.0938 

36.4593 

26 

.4637 

17.8768 

2.1566 

38.5530 

27 

.4502 

18.3270 

2.2213 

40.7096 

28 

.4371 

18.7641 

2.2879 

42.9309 

29 

.4243 

19.1885 

2.3566 

45.2189 

30— 

4120-- 

---19  6004-- 

2.4273- 

47.5754 

31 

.4000 

20.0004 

2.5001 

50.0027 

32 

.3883 

20.3888 

2.5751 

52.5028 

S3 

.3770 

20.7658 

2.6523 

55.  0778 

34 

.3660 

21.1318 

2.7319 

57.7302 

So 

,3554 

21.4872 

2.8139 

60.4621 

36 

.3450 

21.8323 

2.8983 

63.2759 

37 

.3350 

22.1672 

2.9852 

66 . 1742 

38 

.3252 

22.4925 

3.0748 

69 . 1594 

39 

.3158 

22.8082 

3.1670 

72.2342 

40- 

---.3066- 

---23.1148- 

--3. 2620- 

75.4013 

41 

.2976 

23.4124 

3.3599 

78.6633 

42 

.2890 

23.7014 

3.4607 

82.0232 

43 

.2805 

23.9819 

3.5645 

85.4839 

44 

.2724 

24.2543 

3.6715 

89.0484 

45 

.2644 

24.5187 

3.7816 

92.7199 

46 

.2567 

24. 7754 

3.8950 

96.5015 

47 

.2493 

25.0247 

4.0119 

100.3965 

48 

.2420 

25.2667 

4.1323 

104.4084 

49 

.2350 

25.5017 

4.2562 

108.5406 

50- 

—  .2281- 

-.25.7298- 

--4.3839- 

112.7969 

55 

.1968 

26.7744 

5.0821 

136.072 

60 

.1697 

27.6756 

5.8916 

163.053 

65 

.1464 

28.452 

6.8300 

194.333 

70 

.1263 

29.123 

7.9178 

230.594 

75 

.1089 

29.702 

9 . 1789 

272.630 

80 

.0940 

30.201 

10  .6409 

321.363 

85 

.0811 

30.701 

12  .3357 

377.857 

90 

.0699 

31.002 

14.3005 

443.349 

95 

.0603 

31.323 

16.5782 

519.273 

100-- 

0520- 

--31. 599— 

-.-19.2186- 

--607.288 

105 

.0449 

31.838 

22.2797 

709.323 

110 

.0387 

32.043 

25.8282 

827.608 

115 

.0334 

32.220 

29.9420 

964.733 

120 

.0288 

32.373 

34.7110 

1,123.70 

3H  PER  CENT. 


I 

II 

III 

IV 

V 

1 

.9662 

.9662 

1.0350 

1.0000 

2 

.9335 

1.8997 

1.0712 

2.0350 

3 

.9019 

2.8016 

1.1087 

3.1062 

4 

.8714 

3.6731 

1.1475 

4.2149 

6 

.8420 

4.5151 

1 . 1877 

5.3625 

6 

.8135 

5 . 3286 

1.2293 

6.5502 

7 

.7860 

6.1145 

1.2723 

7.7794 

8 

.7594 

6.8740 

1.3168 

9.0517 

9 

.7337 

7.6077 

1.3629 

10.3685 

10_- 

7089.. 

8  3166 

1.4106.. 

-  11  7314 

11 

.6849 

9.0016 

1.4600 

13.1420 

12 

.6618 

9.6633 

1.5111 

14.6020 

13 

.6394 

10.3027 

1.5640 

16.1130 

14 

.6178 

10.9205 

1.6187 

17.6770 

15 

.5969 

11.5174 

1.6753 

19.2957 

16 

.5767 

12.0941 

1.7340 

20.9710 

17 

.5572 

12.6513 

1.7947 

22.7050 

18 

.5384 

13.1897 

1.8575 

24.4997 

19 

.5202 

13.7098 

1.9225 

26.3572 

20 

5026 

14  2124 

1  9898 

-  28  2797 

21 

.4856 

14.6980 

2.0594 

30.2695 

22 

.4692 

15.1671 

2.1315 

32.3289 

23 

.4533 

15.6204 

2.2061 

34.4604 

24 

.4380 

16.0574 

2.2833 

36.6665 

26 

.4231 

16.4815 

2.3632 

38.9499 

26 

.4088 

16.8904 

2.4460 

41.3131 

27 

.3950 

17.2854 

2.5316 

43.7591 

28 

.3817 

17.6670 

2.6202 

46.2906 

29 

.3687 

18.0358 

2.7119 

48.9108 

30.. 

3563.. 

...18.3920.- 

2.8068.. 

51.6227 

31 

.3442 

18.7363 

2.9050 

54.4295 

32 

.3326 

19.0689 

3.0067 

57.3345 

33 

.3213 

19.3902 

3.1119 

60.3412 

34 

.3105 

19.7007 

3.2209 

63.4532 

35 

.3000 

20.0007 

3.3336 

66.6740 

36 

.2898 

20.2905 

3.4503 

70.0076 

37 

.2800 

20.5705 

3.5710 

73.4579 

38 

.2706 

20.8411 

3.6960 

77.0289 

39 

.2614 

21 . 1025 

3.8254 

80.7249 

40.. 

....2526.. 
.2440 

...21.3551.. 
21.5991 

3.9593- 

84.5503 

41 

4.0978 

88.5095 

42 

.2358 

21.8349 

4.2413 

92.6074 

43 

.2278 

22.0627 

4.3897 

96.8487 

44 

.2201 

22.2828 

4.5433 

101.2383 

45 

.2127 

22.4955 

4.7024 

105.7817 

46 

.2055 

22.7009 

4.8669 

110.4840 

47 

.1985 

22.8994 

5.0373 

115.3510 

48 

.1918 

23.0912 

5.2136 

120. 3883 

49 

.1853 

23.2766 

5.3961 

125.6018 

50.. 

—  .1791.. 

-.23.4556.- 

5.5849__ 

130.9979 

55 

.1508 

24.2641 

6.6331 

160.947 

60 

.1269 

24.9447 

7.8781 

196.517 

65 

.1069 

25.5168 

9.3567 

238.763 

70 

0900 

26.0004 

11.1128 

288.938 

75 

.0758 

26.4067 

13.1986 

348.531 

80 

.0638 

26.7488 

15.6757 

419.307 

85 

.0537 

27.0368 

18.6179 

503.368 

90 

.0452 

27.2793 

22.1122 

603.205 

95 

.0381 

27.4798 

26.2623 

721.780 

100  _. 

-.-.0321.. 

-.-27.6554.. 

-. .31. 1914- 

....862.612 

105 

.0270 

27.8002 

37.0456 

1,029.874 

110 

.0227 

27.9221 

43.9986 

1,228.  53 

115 

.0191 

28.0247 

52.2565 

1,464.471 

120 

.0161 

28.1111 

62.0643 

1,744.69 

4  PER  CENT. 


87 


I 

11 

HI 

iin 

V 

1 

.9615 

.9615 

1.0400 

1.0000 

2 

.9246 

1.8861 

1.0861 

2.0400 

3 

.8890 

2.7751 

1 . 1249 

3.1216 

4 

.8548 

3.6299 

1 . 1699 

4.2465 

6 

.8219 

4.4518 

1.2167 

5.4163 

6 

.7903 

5.2421 

1.6253 

6.6330 

7 

.7599 

6.0021 

1.3159 

7.8983 

8 

.7307 

6.7327 

1.3686 

9.2142 

9 

.7026 

7,4353 

1.4233 

10.5828 

10 

6756-- 

8  1109-- 

1 .4802-- 

12.0061 

11 

.6496 

8.7605 

1.5395 

13,4864 

12 

.6246 

9.3851 

1.6010 

15.0258 

13 

.6006 

9.9856 

1.6651 

16.6268 

14 

.5775 

10.5631 

1.7315 

18.2919 

15 

.5553 

11.1184 

1.8009 

20.0236 

16 

.5339 

11.6523 

1.8730 

21.8245 

17 

.5134 

12.1657 

1.9479 

23.6975 

18 

.4936 

12.6593 

2,0258 

25.6454 

19 

.4746 

13.1339 

2 , 1068 

27.6712 

20 

-4564 

1 3  ^903 

2  1911-- 

29.7781 

21 

.4388 

14.0292 

2^2788 

31 '9692 

22 

.4220 

14.4511 

2,3699 

34.2480 

23 

.4057 

14.8568 

2,4647 

36.6179 

24 

.3901 

15.2470 

2,5633 

39.0826 

25 

■  3751 

15.6221 

2,6658 

41.6459 

26 

.3607 

15.9828 

2,7725 

44.3117 

27 

.3468 

16.3296 

2,8834 

47.0842 

28 

.3335 

16.6631 

2.9987 

49.9676 

29 

.3207 

16.9837 

3.1187 

52.9663 

30- 
31 

--.3083- 
.2965 

--17.2920-- 
17.5885 

3.2434-- 

56  0849 

3^3731 

59^3283 

32 

.2851 

17,8736 

3.5081 

62.7015 

S3 

.2741 

18.1476 

3.6484 

66.2095 

34 

2636 

18.4112 

3.7943 

69.8579 

36 

.  2534 

18.6646 

3.9461 

73.6522 

36 

.2437 

18.9083 

4.1039 

77.5983 

37 

.2343 

19.1426 

4.2681 

81.7022 

38 

.2253 

19.3679 

4.4388 

85.7903 

39 

.2166 

19.5845 

4.6164 

90.4091 

40 

2083 

19  7928 

4.8010-- 

95.0255 

41 

.2003 

19^9931 

4.9931 

99.8265 

42 

.1926 

20  .1856 

5 . 1928 

104.8200 

43 

.1852 

20.3708 

5.4005 

110.0124 

44 

.1780 

20.5488 

5.6165 

115.4129 

45 

.1712 

20.7200 

5.8412 

121,0294 

46 

.1646 

20.8847 

6.0748 

126,8706 

47 

.1583 

21.0429 

6.3178 

132,9454 

48 

.1522 

21.1951 

6.5705 

139.2632 

49 

.1463 

21.3415 

6.8333 

145.8337 

50  - 

1407— 

-21.4822-- 

7.1067- 

..-152.6671 

55 

.1157 

22 . 1086 

8.6464 

191.159 

60 

.0951 

22.6235 

10,5196 

237.991 

65 

.0781 

23.0466 

12,7987 

294.967 

70 

.0642 

23.3945 

15,5716 

364.290 

75 

.0528 

23.6281 

18,9453 

448.642 

80 

.0434 

23.9154 

23,0498 

551 . 245 

85 

.0357 

24 . 1085 

28,0436 

676.090 

90 

.0293 

24 . 2673 

34,1193 

827.983 

95 

.0241 

24.3977 

41,5114 

1,012.785 

100.. 

_...0198_. 

__ -24.5050. - 

___50,5049-- 

..1,237.622 

105 

.0163 

24.5931 

61,4470 

1,511.175 

110 

.0134 

24 . 6656 

74.7597 

1,843.992 

115 

.0110 

24.7251 

90.9566 

2,248.915 

120 

.0090 

24.7741 

110.663 

2,741.558 

38 


4H  PER  CENT. 

I 

II 

in 

nil 

V 

1 

.9569 

.9569 

1.0450 

1.0000 

2 

.9157 

1.8727 

1.0920 

2.0450 

3 

.8765 

2.7490 

1.1412 

3.1370 

4 

.8386 

3.5875 

1 . 1925 

4.2782 

6 

.8022 

4.3900 

1.2462 

5.4707 

6 

.7679 

5.1579 

1.3023 

6.7169 

7 

.7348 

5.8927 

1.3609 

8.0192 

8 

.7032 

6.5959 

1.4221 

9.3800 

9 

.6729 

7.2688 

1.4861 

10.8021 

10 

6439 

7  9125 

1  5530 

12  2882 

ll" 

.6162 

8.5289 

1.6229 

13.8412 

12 

.4897 

9.1186 

1.6959 

15.4640 

13 

.5643 

9.6829 

1.7722 

17.1599 

14 

.5400 

10.2229 

1.8519 

18.9321 

15 

.5167 

10.7395 

1.9353 

20.7841 

16 

.4945 

11.2340 

2.0224 

22.7193 

17 

.4732 

11.7072 

2.1134 

24.7417 

18 

.4528 

12.1600 

2.2085 

26.8551 

19 

.4333 

12.5933 

2.3079 

29.0634 

20 

4146 

13  0079 

2.4117.. 

31  3716 

2l" 

.3968 

13^4047 

2.5202 

33.7831 

22 

.3797 

13.7844 

2.6337 

36.3034 

23 

.3634 

14.1478 

2.7522 

38.9370 

24 

.3477 

14.4955 

2.8760 

41.6892 

25 

.3327 

14.8282 

3.0054 

44.5652 

26 

.3184 

15.1466 

3.1407 

47.5706 

27 

.3047 

15.4513 

3.2820 

50.7113 

28 

.2916 

15.7429 

3.4279 

53.9933 

29 

.2790 

16.0219 

3.5840 

57.4230 

30._ 

2670-. 

--16.2889- 

3.7453.. 

61.0071 

31 

.2555 

16.5444 

3.9139 

64.7524 

32 

.2445 

16.7889 

4.0900 

68.6602 

33 

.2340 

17.0229 

4.2740 

72.7562 

34 

.2239 

17.2468 

4.4664 

77.0303 

35 

.2143 

17.4610 

4.6673 

81.4966 

36 

.2050 

17.6660 

4.8774 

86.1640 

37 

.1962 

17.8622 

5.0969 

91.0413 

38 

.1878 

18.0500 

5.3262 

96.1382 

39 

.1797 

18.2297 

5.5659 

101.4644 

40__ 

.._.1719_- 

-.18.4016- 

5.8164.. 

....107.0303 

41 

.1645 

18.5661 

6.0781 

112.8467 

42 

.1574 

18.7235 

6.3516 

118.9248 

43 

.1507 

18.8742 

6.6374 

125.2764 

44 

.1442 

19.0184 

6.9361 

131.9138 

45 

.1380 

19.1563 

7.2482 

138.8500 

46 

.1320 

19.2884 

7.5744 

146.0982 

47 

.1263 

19.4147 

7.9153 

153.6726 

48 

.1209 

19.5356 

8.2715 

161.5879 

49 

.1157 

19.6513 

8.6437 

169.8594 

50 

..  .1107._ 
.0888 

19.7620 

—  9.0326.. 

178.5030 

55 

20.2480 

11.2563 

227.9180 

60 

.0713 

20.6380 

14.0274 

289.4980 

65 

.0572 

20.9509 

17.4807 

366.2380 

70 

.0459 

21.2021 

21.7841 

461.8700 

75 

.0368 

21.4118 

27.1470 

581.2670 

80 

.0296 

21.5653 

33.8301 

729.5580 

85 

.0237 

21.6951 

42.1585 

914.6330 

90 

.0190 

21.7992 

52.5371 

1145.2700 

95 

.0153 

21.8828 

65.4708 

1432.6840 

100  __ 

_...0123__ 

-.21.9499- 

.. .81.5885.. 

...1790.8600 

105 

.0098 

22.0036 

101.674 

2237.2000 

110 

.0079 

22.0468 

126.704 

2793.4300 

115 

.0063 

22.0815 

157.897 

3486.6000 

120 

.0051 

22.1093 

196.768 

4350.4000 

5  PER  CENT. 


39 


I 

II 

III 

nil 

V 

1 

.9524 

.9524 

1.0500 

1.0000 

2 

.9070 

1.8594 

1.1025 

2.0500 

3 

.S63S 

2.7232 

1.1576 

3.1525 

4 

.  S227 

3.5460 

1.2155 

4.3101 

5 

.  7835 

4.3295 

1.2763 

5.5256 

6 

.7462 

5.0757 

1.3401 

6.8019 

7 

.7107 

5.7864 

1.4071 

8.1420 

8 

.6768 

6.4632 

1.4775 

9.5491 

9 

.6446 

7.1078 

1.5513 

11.0266 

10 

6139 

7.7217-- 

1  6289 

12.5779 

ll" 

""";5847" 

8 '3064 

1.7103 

14.2068 

12 

.5568 

8.8623 

1.7959 

15.9171 

13 

.5303 

9.3936 

1.8856 

17.7130 

14 

.5051 

9.8986 

1.9799 

19.5986 

15 

.4810 

10.3797 

2.0789 

21.5786 

16 

.4581 

10.8378 

2.1829 

23.6575 

17 

.4363 

11.2741 

2.2920 

25.8404 

18 

.4155 

11.6896 

2.4066 

28.1324 

19 

.3957 

12.0853 

2.5270 

30.5390 

20 

_ .3769-_ 

12  4622 

.-2.6533-- 

33.0660 

2l'" 

'"';35S9" 

"""l2;8212  ' 

2.7860 

35.7193 

22 

.3418 

13.1630 

2.9253 

38.5052 

23 

.3256 

13.4886 

3.0715 

41.4305 

24 

.3101 

13.7986 

3.2251 

44.5020 

25 

.2953 

14.0939 

3.3864 

47.7271 

26 

.2812 

14.3752 

3.5557 

51.1135 

27 

.2678 

14.6430 

3.7335 

54.6691 

28 

.2551 

14.8981 

3.9201 

58.4026 

29 

.2429 

15.1411 

4.1161 

62 . 3227 

30 

2314 

15.3725__ 

4  3219 

66.4388 

31  ' 

"'^2204' 

""'15.5928 

4.5380 

70.7608 

32 

.2099 

15.8027 

4.7649 

75.2988 

33 

.1999 

16.0025 

5.0032 

80.0638 

34 

.1904 

16.1929 

5.2533 

85.0670 

35 

.1813 

16.3742 

5.5160 

90.3203 

36 

.1727 

16.5469 

5.7918 

95.8363 

37 

.1644 

16.7113 

6.0814 

101.6281 

38 

.1566 

16.8679 

6.3855 

107.7095 

39 

.1491 

17.0170 

6.7048 

114.0950 

40_. 

-...1420-_ 

.._17.1591.- 

7.0400-. 

120.7998 

41 

.1353 

17.2944 

7.3920 

127.8398 

42 

.1288 

17.4232 

7.7616 

135.2318 

43 

.  1227 

17.5459 

8.1497 

142.9933 

44 

.1169 

17.6628 

8.5572 

151.1430 

45 

.1113 

17.7741 

8.9850 

139.7002 

46 

.1060 

17.8801 

9.4343 

168.6852 

47 

.  1009 

17.9810 

9.9060 

178.1194 

48 

.0961 

18.0772 

10.4013 

188.0254 

49 

.0916 

18.1687 

10.9213 

198.4267 

50_. 

..-.0872-_ 

_. .18. 2559- 

..-11.4674.. 

209.3480 

55 

.0683 

18.6335 

14.6356 

272.7130 

60 

.0535 

18.9293 

18.6792 

353.5840 

65 

.0419 

19.1191 

23.8399 

456.7980 

70 

.0329 

19.3427 

30.4264 

588.5290 

75 

.0257 

19.4849 

38.8327 

756.6540 

80 

.0202 

19.5965 

49.5614 

971.2290 

85 

.0158 

19.6838 

63.2544 

1,245.0880 

90 

.0124 

19.7523 

80.7304 

1,594.6100 

95 

.0097 

19.8058 

103.035 

2,040.7000 

100 

0076 

19 . 8479 .  . 

..131.501... 
167.833 

..2,610.0300 

105 

.0060 

19.8808 

3,336.6600 

110 

.0047 

19.9066 

214.202 

4,264.0300 

115 

.0037 

19.9268 

273.382 

5,447.6400 

120 

.0029 

19.9427 

348.912 

6.958.2400 

40 


6M  PSR  CENT. 


I 

u         1           nx 

iiii 

V 

1 

.9479 

.9479 

1.0550 

1.0000 

2 

.8985 

1.8463 

1.1130 

2.0550 

3 

.8516 

2.6979 

1.1742 

3.1680 

4 

.8072 

3.5052 

1.2388 

4.3423 

5 

.7651 

4.2703 

1.3070 

5.5811 

6 

.7252 

4.9955 

1.37S8 

6.SSS1 

7 

.6854 

5.6830 

1.4547 

8.2689 

8 

.6516 

6.3346 

1.5347 

9,7216 

9 

.6176 

6.9522 

1.6191 

11,2563 

10- 

5854  — 

7.5376— 

1.7081-- 

12,8754 

11 

.5549 

8.0925 

1,8021 

14,5835 

12 

.5260 

8.6185 

1,9012 

16.3856 

13 

.4986 

9.1171 

2,0058 

18.2868 

14 

.4726 

9.5896 

2.1161 

20.2928 

15 

.4479 

10.0376 

2,2325 

22.4087 

16 

.4246 

10.4622 

2,3553 

•      24.6411 

17 

.4024 

10.8648 

2.4848 

26.9964 

18 

.3815 

11.2461 

2.6215 

29.4812 

19 

.3616 

11.6077 

2.7656 

32.1027 

20- 

--3427- 

-_11.9501- 

2.9178- 

34.8683 

21 

.3249 

12.2752 

3.0782 

37.7881 

22 

,3079 

12.5S32 

3.4275 

40.8643 

23 

.2919 

12.8750 

3.4262 

44.1118 

24 

.2767 

13.1517 

3.6146 

47.53S0 

25 

.2622 

13.4139 

3.8134 

51.1526 

26 

.2486 

13.6625 

4.0231 

5f.9660 

27 

.2356 

13.8981 

4.2444 

58.9891 

23 

.2233 

14.1214 

4.4778 

03.2335 

29 

.2117 

14.3331 

4.7241 

67.7114 

30- 

--2008- 
.1902 

--14.5337- 
14.7239 

--     4.9840 

71.1355 

31 

5.2581 

77.4194 

32 

.  1803 

14.9042 

5.5473 

82.6775 

33 

.1709 

15.0751 

5.8524 

88.2248 

34 

.1620 

15.2370 

6.1742 

94.0771 

35 

.  1535 

15,3908 

6.5138 

100.2514 

38 

.1455 

15,5361 

6.8721 

106.7652 

37 

.1379 

15.6740 

7.2501 

113.6373 

38 

.1307 

15.8047 

7.6488 

120.8873 

39 

.1239 

15.9287 

8.0695 

128.5381 

40- 

1175- 

-.16.0461- 

--8. 5133- 

136,6056 

41 

.1113 

16.1575 

8.9815 

145,1189 

42 

.1055 

16.2630 

9.4755 

154,1005 

43 

.1000 

16.3630 

9.9967 

163,5760 

44 

.0948 

16.4579 

10,5465 

173,5727 

45 

.0899 

16.5477 

11,1266 

184,1192 

46 

.0852 

16.6329 

11,7385 

195,2457 

47 

.0807 

16.7137 

12,3841 

206,9842 

48 

.0765 

16.7902 

13,0653 

219,3684 

49 

.0725 

16.8628 

13,7838 

232,4336 

50- 

--.0688- 

-.16.9315- 

--14,5420- 

246.2175 

55 

.0526 

17.2251 

19,0046 

327.3563 

60 

.0403 

17.4498 

24,8381 

433.4200 

65 

.0308 

17.6216 

32,4623 

572.0384 

70 

.0230 

17.7630 

43,4150 

771.1818 

75 

.0176 

17.8614 

56.7414 

1,013.4800 

80 

.0138 

17.9309 

72,4703 

1,299.4600 

85 

.0106 

17.9898 

94,7152 

1,703.9127 

90 

.0081 

18.0349 

123,7883 

2,232.5145 

95 

.0062 

18.0694 

161,7855 

2,923.3727 

100- 

0047- 

-  .18.0958- - 

-211.4463- 

-3.826.2963 

105 

.0036 

18.1160 

276.3503 

5,008.3691 

110 

.0028 

18.1315 

361.2768 

6,550.4873 

115 

.0021 

18.1433 

472.0413 

8,564.3873 

120 

.0016 

18.1523 

616.9357 

11,198.8309 

6  PER  CENT. 

I 

II 

Ill 

nil 

1            ^ 

1 

.9434 

.9434 

1.0600 

1 , 0000 

2 

.8900 

1.8334 

1 . 1236 

2 , 0600 

3 

.8396 

2.6730 

1.1910 

3,1836 

4 

.7921 

3.4651 

1.2625 

1            4.3746 

6 

.7473 

4.2124 

1.3382 

1             5.6371 

6 

.7050 

4.9173 

1.4185 

1             6,9753 

7 

.6651 

5.5824 

1.5036 

j            8.3938 

8 

.6274 

6.2098 

1.5938 

1             9.8975 

9 

.5919 

6.8017 

1         1.6895 

11.4913 

10-. 

....5584.. 

7.3601.. 

:.... 1.7908.. 

13.1808 

11 

.5268 

7.8869 

1.8983 

14.9716 

12 

.4970 

8.3838 

2.0122 

16.8699 

13 

.4688 

8.8527 

2.1329 

18.8821 

14 

.4423 

9.2950 

2.2609 

21.0151 

15 

.4173 

9.7122 

2.3966 

23 . 2760 

16 

.3936 

10.1059 

2.5404 

25.6725 

17 

.3714 

10.4772 

2.6928 

28.2129 

18 

.3503 

10.8276 

2.8543 

30,9057 

19 

.3305 

11.1581 

3.0256 

33 . 7600 

20„ 

....3118.. 
.2942 

__.l 1.4699.. 
11.7641 

....3.2071.. 

36.7856 

21 

3.3996 

39.9927 

22 

.2775 

12.0416 

3.6035 

43.3923 

23 

.2618 

12.3034 

3.8197 

46.9958 

24 

.2470 

12.5504 

4.0489 

50.8156 

26 

.2330 

12.7834 

4.2919 

54.8645 

26 

.2198 

13.0032 

4.5494 

59.1564 

27 

.2074 

13.2105 

4.8223 

63 . 7058 

28 

.1956 

13.4062 

5.1117 

68.5281 

29 

.1846 

13.5907 

5.4184 

73.6398 

30._ 

.  ..1741.. 
.1643 

...13.7648.. 

5.7435 

79,0582 

84.8017 

31 

13.9291 

6.0881' 

32 

.1550 

14.0840 

6.4534 

90.8S98 

33 

.1462 

14.2302 

6.8406 

97.3432 

34 

.1379 

14.3681 

7.2510 

104.1838 

35 

.1301 

14.4982 

7.6861 

111.4348 

36 

.1227 

14.6210 

8.1473 

119.1209 

37 

.1158 

14.7368 

8.6361 

127.2681 

38 

.1092 

14.8460 

9.1543 

135.9042 

39 

.1031 

14.9491 

9.7035     ' 

145.0585 

40.. 

....0972.. 

...15.0463__ 

...10.2857.. 

154.7620 

41 

.0917 

15.1380 

10.9029 

165.0477 

42 

.0865 

15.2245 

11.5570     : 

175.9505 

43 

.0816 

15.3062 

12.2505     1 

187.5076 

44 

.0770 

15.3832 

12.9855     j 

199 . 7580 

46 

.0727 

15.4558 

13.7646     i 

212.7435 

46 

.0685 

15.5244 

14.5905 

226,5081 

47 

.0647 

15.5890 

15.4659 

241.0985 

48 

.0610 

15.6500 

16.3939 

256.5645 

49 

.0575 

15.7076 

17.3775 

272.9584 

60.. 

....0543.. 

...15.7619.. 

...18.4202.. 

290.3359 

66 

.0406 

15.9905 

24.6507 

394.1783 

60 

.0303 

16.1611 

32.9883 

533.1383 

65 

.0226 

16.2891 

14.1458 

719.0966 

70 

.0169 

16.3845 

159.0772 

967.9533 

75 

.0126 

16.4558 

1  79.0587 

1,300.9783 

80 

.0095 

16.5091 

105.7985 

1,746.6416 

85 

.0071 

16.5489 

141.5827 

2,343.0450 

90 

.0053 

16.5787 

189.4698 

3,141.1633 

96 

.0039 

16.6009     ' 

253.5538     , 

4,209.2300 

100.. 

....0029..' 

...16.6175..' 

.-339.3125... 

-5,638.5416 

106 

.0022 

16.6299     1 

454.0770     ' 

7,551.2833 

110 

.0016 

16.6392     1 

607.6591 

10,110,9850 

115 

.0012 

16.6461     i 

813.1867 

13,536.4450 

120 

.0009     ' 

16.6513     ! 

1,088,2280 

18,120.4667 

41 


42 


7  PER  CENT. 


I 

II 

III 

iiii 

V 

1 

.9346 

.9328 

1.0700 

1.0000 

2 

.8736 

1.8043 

1 . 1449 

2.0700 

3 

.8163 

2.6228 

1.2250 

3.2142 

4 

.7629 

3.3857 

1.3108 

4.4400 

6 

.7130 

4.0986 

1.4026 

5.7514 

6 

.6663 

4.7657 

1.5007 

7.3529 

7 

.6227 

5.3886 

1.6058 

8.6542 

8 

.5820 

5.9700 

1.7182 

10.2600 

9 

.6439 

6.5143 

1.8385 

11.9786 

10- 
11 

5083-- 

7.0228— 

--  1  9671 

13  8159 

.4751 

7.4971 

2.1049 

15.7843 

12 

.4440 

7.9414 

2.2522 

17.8886 

13 

.4150 

8.3557 

2.4098 

20.1400 

14 

.3878 

8.7442 

2.5785 

22.5500 

16 

.3624 

9.1071 

2.7590 

25.1286 

16 

.3387 

9.4457 

2.9522 

27.8886 

17 

.3161 

9.7686 

3.1588 

30.8400 

18 

.2959 

10.0571 

3.3800 

34.0000 

19 

.2765 

10.3343 

3.6165 

37.3786 

20- 
21 

2584  — 

-..10.5928-- 

3.8697-- 

40  9528 

.2415 

10.8343 

4.1406 

44.8657 

22 

.2257 

11.0600 

4.4304 

49.0057 

23 

.2109 

11.2714 

4.7405 

63.4343 

24 

.1971 

11.4685 

5.0724 

55.3200 

25 

.1842 

11.6528 

5.4275 

63.2500 

26 

.1722 

11.8242 

5.8075 

68.6786 

27 

.1609 

11.9857 

6.2140 

74.4857 

28 

.1504 

12.1357 

6.6490 

80.7000 

29 

.1406 

12.2757 

7.1144 

87 . 3346 

30- 
31 

.1314-- 

12  4071 

7  6124 

94.4628 

""!l228 

12.5300 

8.1452 

102.0742 

32 

.1147 

12.6457 

8.7154 

110.2700 

33 

.1072 

12.7528 

9.3255 

118.9500 

34 

.1002 

12.8528 

9.9783 

128.2618 

36 

.0937 

12.9457 

10.6768 

138.2400 

36 

.0875 

13.0343 

11.4241 

148.9157 

37 

.0818 

13.1157 

12.2239 

160.3414 

38 

.0765 

13.1914 

13.0795 

172.5642 

39 

.0715 

13.2628 

13.9960 

185.6428 

40- 

-..0668- 

...13.3300.. 

...14.9747.. 

-- 199. 6386 

41 

.0624 

13.3928 

16.0230 

214.6143 

42 

.0583 

13.4514 

17.1446 

230.6371 

43 

.0545 

13.5057 

18.3448 

247.7828 

44 

.0509 

13.5571 

19.6290 

266.1428 

46 

.0476 

13.6043 

21.0030 

285.7571 

46 

.0445 

13.6485 

22.4332 

306.1886 

47 

.0416 

13.6900 

24.0463 

329.2328 

48 

.0387 

13.7314 

26.7888 

364.1257 

49 

.0363 

13.7657 

27.5306 

379.0086 

80- 

-..0339- 

...13.8000.. 

...29.4577- 

- -406. 5386 

66 

.0242 

13.9385 

41.3162 

576.9458 

60 

.0173 

14.0371 

57.9482 

813.6468 

66 

.0123 

14.1085 

81.2755 

1146.7928 

70 

.0088 

14.1585 

113.9929 

1614.1844 

75 

.0062 

14.1959 

159.8823 

2141.1767 

80 

.0045 

14.2200 

224.2440 

2269.7471 

86 

.0032 

14.?385 

314.5138 

3160.6286 

90 

.0023 

14.2514 

441 . 1230 

4478.7682 

95 

.0016 

14.2614 

618.7000 

6287.4714 

100. 

0011.. 

...14.2685.. 

..867.7600- 

...8824.2867 

106 

.0008 

14.2728 

1217.0812 

12382.2855 

110 

.0006 

14.2757 

1707.0235 

17372.6886 

116 

.0004. 

14.2785 

2394.1978 

24371.7642 

120 

.0003 

14.2800 

3357.9923 

34188.5400 

8  PER  CENT. 


4S 


I 

11 

in 

nil 

V 

1 

.9259 

.9250 

1.0800 

1.0000 

2 

.8573 

1.7825 

1.1664 

2.0800 

3 

.7938 

2.5762 

1.2597 

3.2463 

4 

.7350 

3.3112 

1.3605 

4.5062 

6 

.6806 

3.9912 

1.4693 

6.8366 

6 

.6302 

4.6212 

1.5869 

7.3362 

7 

.5840 

5.1987 

1.7138 

8.9225 

8 

.5403 

5.7450 

1.8509 

10.6363 

9 

.5002 

6.2462 

1.9990 

12.4875 

10- 

4632- 

6.7087 

2  1589 

14  4862 

11 

.4289 

7.1375 

2.3317 

""'l6;6463 

12 

.3971 

7.5350 

2.5182 

18.9775 

13 

.3676 

7.9037 

2.7196 

21.4950 

14 

.3405 

8.2425 

2.9372 

24.2150 

15 

.3152 

8.5587 

3.1722 

27.1525 

16 

.2919 

8.85-13 

3.4260 

30.3250 

17 

.2703 

9.1200 

3.7000 

33.7500 

18 

.2502 

9.3712 

3.9960 

37.4500 

19 

.2317 

9.6025 

4.3157 

41.4463 

20- 

2145-- 

9.8175-- 

4  6610 

45.7625 

21 

.1987 

10.0150 

5.0339 

50.4237 

22 

.1839 

10.2000 

5.4366 

55.4575 

23 

.1703 

10.3700 

5.8716 

60.8950 

24 

.1577 

10.5275 

6.3413 

66.7663 

25 

.1460 

10.6737 

6.8486 

73.1075 

26 

.1352 

10,8087 

7.3964 

79.9800 

27 

.1252 

10.9337 

7.9882 

87.3525 

28 

.1159 

11.0500 

8.6272 

95.3400 

29 

.1073 

11.1575 

9.3174 

103.9675 

30- 

--.0994- 
.0920 

-.11.2562- 
11.3487 

10  0629 

113  2862 

31 

10.8678 

123.3475 

32 

.0852 

11.4337 

11.7371 

134.2138 

33 

.0789 

11.5125 

12.6763 

145.9537 

34 

.0730 

11.5862 

13.6904 

158.6300 

36 

.0676 

11.6537 

14.7853 

172.3163 

36 

.0626 

11.7162 

15.9684 

187.1050 

37 

.0580 

11.7737 

17.2460 

203.0750 

38 

.0537 

11.8275 

18.6249 

220.3113 

39 

.0497 

11.8775 

20.1159 

238.9488 

40- 

-..0460- 
.0426 

-.11.9237- 
11.9662 

...21. 7250.. 

-259.0625 

41 

23.4630 

280.7876 

42 

.0395 

12.0050 

25.3400 

304.2500 

43 

.0365 

12.0425 

27.3672 

329.5900 

44 

.0338 

12.0762 

29.5567 

356.9588 

45 

.0313 

12.1075 

31.9213 

386.5163 

46 

.0290 

12.1362 

34.4750 

418.4376 

47 

.0269 

12.1625 

37.2330 

452.9125 

48 

.0249 

12.1875 

40.2117 

490.1463 

49 

.0230 

12.2112 

43.4207 

530.2588 

50- 

0213- 

.0145 

-.12.2325- 
12.3175 

46  9029  - 

573.7863 

66 

68.9160 

848.9500 

60 

.0099 

12.3750 

101.2605 

1253.2563 

66 

.0067 

12.4150 

148.7849 

1847.3113 

70 

.0046 

12.4412 

218.6150 

2720.1875 

76 

.0031 

12.4600 

321.2177 

4002.7213 

80 

.0021 

12.4725 

471.9761 

5887.2013 

85 

.0014 

12.4812 

693.4888 

8656.1100 

90 

.0010 

12.4862 

1018.9649 

12724.5613 

96 

.0007 

12.4900 

1497.1993 

18702.4913 

100- 

-..0005- 

.  —  12.4925- 

-2199.8838.. 

,.27486.0476 

105 

.0003 

12.4950 

3232.3656 

40392.0700 

110 

.0002 

12.4962 

4749.4130 

59355.1625 

115 

.0001 

12.4975 

6978.4677 

87218.3463 

120 

.0001 

12.4975 

10253.6792 

128158.4900 

44 


10  PER  CENT. 

I 

II 

Ill 

iiii 

V 

1 

.9091 

0.908 

1 . 1000 

1.0000 

2 

.8264 

1.735 

1.2100 

2.1000 

3 

.7513 

2.486 

1.3310 

3.3100 

4 

.6830 

3.169 

1.4641 

4.6410 

6 

.6209 

3.790 

1.6105 

6.1050 

6 

.5645 

4.354 

1.7716 

7.7160 

7 

.5132 

4.867 

1.9487 

9.4870 

8 

.4665 

5.334 

2.1436 

11.4360 

9 

.4241 

5.758 

2.3580 

13.5800 

10- 

3855_. 

6.144.— 

2.5938- 

15.9380 

11 

.3505 

6.494 

2.8531 

18.5310 

12 

.3186 

6.813 

3.1385 

21.3850 

13 

.2897 

7.102 

3.4523 

24.5230 

14 

.2633 

7.366 

3.7976 

27.9760 

15 

.2394 

7.605 

4.1773 

31.7730 

16 

.2176 

7.823 

4.5950 

35.9500 

17 

.1978 

8.021 

5.0545 

40.5450 

18 

.1799 

8.200 

5.5600 

45.6000 

19 

.1635 

8.364 

6.1160 

51 . 1600 

20- 

1486— 

8  513 

--.  6.7276 

57.2760 

21 

.1351 

8.648 

7.4004 

64.0040 

22 

.1228 

8.771 

8.1404 

71.4040 

23 

.1117 

8.882 

8.9545 

79.5450 

24 

.1015 

8.984 

9.8500 

88.6000 

25 

.0923 

9.076 

10.8349 

98.3490 

26 

.0839 

9.160 

11.9184 

109 . 1840 

27 

.0763 

9.236 

13.1103 

121.1030 

28 

.0693 

9.306 

14.4213 

134.2130 

29 

.0630 

9.369 

15.8634 

148.G340 

30- 

-_.0573- 

--9.426-. 

.--17.4498.- 

-..164.4980 

31 

.0521 

9.478 

19.1948 

181.9480 

32 

.0474 

9.525 

21.1143 

201 . 1430 

33 

.0431 

9.568 

23.2257 

222.2570 

34 

.0391 

9.608 

25.5483 

245.4830 

35 

.0356 

9.643 

28.1032 

271.0320 

36 

.0324 

9.675 

30.9135 

299.1350 

37 

.0294 

9.705 

34.0049 

330.0490 

38 

.0273 

9.726 

37.4054 

364.0540 

39 

.0243 

9.756 

41 . 1460 

401.4600 

40-. 

-..0221- 

. 9.778-. 

...45.2605- 

442.6050 

41 

.0201 

9.798 

49.7866 

487.8660 

42 

.0183 

9.816 

54.7655 

537.6550 

43 

.0166 

9.833 

60.2420 

592.4200 

44 

.0151 

9.848 

66.2662 

652.6620 

45 

.0137 

9.862 

72.8928 

718.9280 

46 

.0125 

9.874 

80.1822 

791.8220 

47 

.0113 

9.886 

88.2004 

872.0040 

48 

.0103 

9.896 

97.0207 

960.2070 

49 

.0094 

9.905 

106.7228 

1057.2280 

50- 

—  0085- 

....9.914... 

-117.3926- 

..-1163.9260 

55 

.0053 

9.946 

189.0668 

1880.6680 

60 

.0033 

9.966 

304.4944 

3034.9440 

65 

.0020 

9.979 

490.3932 

4893.9320 

70 

.0013 

9.986 

789.7876 

7887.8760 

75 

.0008 

9.991 

1271.9648 

12709.6480 

80 

.0005 

9.994 

2048.5188 

20475.1880 

85 

.0003 

9.996 

3299 . 1742 

32981.7420 

90 

.0002 

9.997 

5313.3659 

53123.6590 

95 

.0001 

9.998 

8557.2549 

85562.5490 

100- 

.00007a 

9.9992.- 

9.9994 

13781.6139- 
22195.5102 

137806.1390 

105 

.00005 

221945.1020 

110 

.00003 

9.9996 

35746.1983 

357451.9830 

115 

.00002 

9.9997 

57569.8666 

575688.6660 

120 

.00001 

9.9998 

92717.0213 

927160.2130 

